A police official identified the suspect as Richard Henry Bain, 62, from La Conception, Quebec. The police official spoke to The Associated Press on condition of anonymity because the suspect has not been charged yet.
Quebec provincial police earlier Wednesday said a masked gunman wearing a bathrobe opened fire just outside the building where Pauline Marois of the separatist Parti Quebecois was giving her victory speech.
The gunman was heard shouting "The English are waking up!" in French as police dragged him away.
Marois was whisked off the stage by guards while giving her speech and was not injured.
"I am deeply affected by this but I have to go forward and assume my responsibilities," Marois said Wednesday.
"In spite of this tragedy we must say Quebec is a non-violent society. An act of folly cannot rid us of this reality," she added.
Marois, who at 63 became Quebec's first female premier, called the shooting an isolated event and said it was probably a case of person that "has serious health issues."
When she first went back stage, Marois said she saw that somebody was wounded and that there was a fire outside, but she thought everything was under control. Police said the suspect lit a small fire before he was arrested.
It was not clear if the gunman was trying to shoot Marois, whose party favors separation from Canada for the French-speaking province.
Lieut. Guy Lapointe of the Quebec provincial police said earlier the suspect was taken to a hospital during the interrogation, but his life was not in danger.
"We can't establish at this point what the motive or intent was. Was he targeting Madame Marois? I'll tell you a lot of things were said by this individual after they arrested him, in French and English," Lapointe said.
Police had dealt with the suspect previously for a minor incident, Lapointe said.
Marois was giving her victory speech to hundreds of supporters at the Metropolis auditorium. She had just declared her firm conviction that Quebec needs to be a sovereign country before she was pulled off the stage.
"What's going on?" Marois told her security detail as they grabbed her arms and dragged her away during the celebration of her party's victory in Tuesday's provincial election.
Police initially said the gunman made it into the building, but now believe he opened fired just outside in the back alley. The gunman then set a small fire before he was captured, police said. Lapointe said he didn't put up any resistance.
Marois returned to the stage after the shooting and asked the crowd to disperse peacefully, and then seemed to finish her speech. She left the hall amid a tight cordon of provincial police bodyguards.
The attack shocked Canadians who are not used to such violence at political events.
There has been an unusual series of high-profile shootings in Canada this year, including one at a Toronto shopping mall popular with tourists. Canadians have long worried that gun violence more often seen in the U.S. could become more common in their country.
That last outbreak of major political violence in Quebec occurred in the 1970s when Canadian soldiers were deployed because of a spate of terrorist acts by a group seeking independence.
In 1970, members of the militant FLQ kidnapped and killed Quebec's labor minister and later abducted, then freed, a British diplomat.
The subsequent "October Crisis" was considered one of the darkest periods in modern Canadian history. Canadian troops patrolled the streets of Quebec and jailed alleged FLQ sympathizers, most of whom were later found innocent of having any FLQ ties.
The suspect in Tuesday's shooting was a heavy-set man wearing a black ski or balaclava mask, glasses and a blue bathrobe over a black shirt and black shorts. Police didn't identify what weapons he had, but camera footage showed a pistol and a rifle at the scene. Police said there is no reason to believe anyone else was involved.
Police said a 48-year-old man was pronounced dead at the scene and a 27-year-old man was wounded but would survive. A third man was treated for shock. Police didn't identify the victims, but they worked at production company Productions du Grand Bambou Inc, a person answering the phone at the Montreal company confirmed.
The crowd was apparently unaware of what happened when Marois was whisked off the stage.
Canadian Prime Minister Stephen Harper said in a statement that he was "angered and saddened" by the shooting.
"It is a tragic day where an exercise of democracy is met with an act of violence," Harper said. He added, "This atrocious act will not be tolerated and such violence has no place in Canada."
Harper said he spoke with Marois.
Jean Charest, who lost to Marois in the election after ruling Quebec for nearly a decade, said he was he was "very saddened" by the shooting.
Police said investigators did preliminary search of the suspect's vehicle to determine whether it contained explosives and were going through it again in their hunt for clues.
Bain owns a hunting and fishing resort near the ski resort area of Mont Tremblant, Quebec, about 90 miles (145 kilometers) north of Montreal.
A list of members of the Mont Tremblant Chamber of Commerce describes Richard Bain as the owner of Les ActivitTs Rick, which promotes itself as a major fly-fishing destination. The site, however, was pulled down Wednesday with the message "This account has been suspended." The phone number listed was out of service.
Marie-France Brisson, director general in the municipality of La Conception, said Bain was a busy local businessman who frequently met with community officials, notably to expand his outdoor activities. His requests included exclusive rights to local land, which involved complicated processes that sometimes frustrated Bain, she said.
Brisson said Bain dealt with them in French, not English, though it was broken French. He complained about red tape, but there were no outbursts about language, she adde.d Brisson said she last saw Bain in recent weeks and there was no change in his usual demeanor.
Jean Benoit Daigneault, of tour and charter helicopter company Heli-tremblant, said the two met on a few occasions, but he wasn't aware of any grief Bain had with the PQ.
The separatist party won Tuesday's provincial election but failed to win a majority of legislative seats.
Though the Parti Quebecois wants the province to break away from Canada, its victory is unlikely to signal a new push for independence. Opinion polls show little appetite for a separatist referendum. Previous referendums on separatism were rejected by voters in 1980 and 1995.?
Analysts said the PQ victory had more to do with weariness with the Liberals after three terms.
Marois herself has left much uncertainty about if and when a referendum would be held. But her party will push for more autonomy from the federal government.
The attack took place just after Marois began speaking in English -- a rare occurrence in a speech at a partisan PQ event. She had promised English-speaking Quebecers that their rights would be protected, following an emotionally charged campaign that saw her party focus on language-and-identity issues.
Earlier in the evening, people in the crowd booed when they heard Charest speak English in his concession speech.
The PQ has said it would seek a transfer of powers from the federal government in areas like employment insurance and immigration policy. If those measures are rejected, the party believes it would have a stronger case for independence.
Before the shooting, Charest, who lost his own assembly seat, congratulated Marois on becoming Quebec's first female premier. He noted that she would be leading a minority government and said the results speak "to the fact that the future of Quebec lies within Canada." He did not indicate whether he would step down as Liberal leader after the defeat.
Charest called the election more than a year before he had to, citing unrest in the streets due to student protests earlier this year over tuition hikes.
Marois said Wednesday she is cancelling the tuition hikes.
Marois was first elected to Quebec's National Assembly in 1981. She retired in 2006 but returned to become PQ leader a year later after her predecessor lost to Charest in an election that landed the PQ in third place. She in turn lost to Charest in 2008.
Gillies reported from Toronto.