The interview with Palin was confirmed Friday, ABC News spokesman Jeffrey Schneider said.
The first-term Alaska governor has given speeches alongside McCain since becoming his surprise pick on Aug. 29. But Democrats have already begun to question why Palin has not been put before reporters to answer questions.
McCain, who appeared on CBS' "Face the Nation" Sunday, said he expected Palin to start doing interviews "in the next few days."
McCain campaign manager Rick Davis complained that the media has focused too much on 44-year-old Palin's personal life. Many of those stories came after McCain's campaign announced that Palin's unwed 17-year-old daughter was pregnant. News reports also have questioned her record as a reformer in Alaska.
"She's not scared to answer questions," Davis said on "Fox News Sunday." "But you know what? We run our campaign, not the news media. And we'll do things on our timetable."
The interview is a coup for Gibson, who also had the only sit-down with McCain during the Republican National Convention.
During that interview, he did not question McCain about Palin's family, a decision that he fretted about for hours, Gibson said in a Web log posted last week.
"Once you know about her daughter's pregnancy, once you know about her husband's political interest in the Alaska Independent Party, once you know about the special nature of their latest child, I think that's enough," Gibson wrote.
The relevant questions about Palin all related to her experience and policy positions as a mayor and governor of Alaska.
ABC News spokesman Jeffrey Schneider said he did not believe Gibson's stated stance about family questions was key to securing the interview.
Salter said the offer was made the day after the Republican convention and that there were no ground rules on what could be asked.
He also said Palin had not been sent out to campaign on her own because McCain enjoyed the excitement she was injecting into his campaign.
"They're having a good time. We were riding a lot of momentum coming out of the convention. The crowds were large," said Salter. "The senator himself thought they should continue on for a few days."
Palin won over GOP loyalists with her speech last week at the Republican convention in St. Paul, Minn., which drew more than 40 million television viewers. But Democrats and even some Republicans have questioned whether she is ready to answer unscripted questions about national and international issues.
"Why would we want to throw Sarah Palin into a cycle of piranhas called the news media that have nothing better to ask questions about than her personal life and her children?" Davis said. "So until at which point in time we feel like the news media is going to treat her with some level of respect and deference, I think it would be foolhardy to put her out into that kind of environment."
Palin's Democratic counterpart, Sen. Joe Biden, a veteran of the Sunday talk show circuit, challenged Palin to sit for interviews.
"Eventually she's going to have to sit in front of you like I'm doing and have done," Biden said on "Meet the Press" on NBC. "Eventually she's going to have to answer questions and not be sequestered. Eventually she's going to have to answer questions about her record."
Gibson, in the Web log posted the day after Palin's speech, said he thought it was a very successful night for her.
"The difficult hurdles are to come, I think: The first interviews she'll face on issues; the first time she's closely questioned on positions she's taken in her state; and then, of course, the debate with Joe Biden," he wrote.
Associated Press writers Darlene Superville in Washington and Sara Kugler in Kansas City, Mo., contributed to this report.