Ose said in a statement on Tuesday that he was treated for a heart attack at Mercy General Hospital in Sacramento on Sunday.
The Republican candidate said that while he is expected to recover, additional procedures may be necessary, and he must focus on healing.
"Sometimes you have to do things you don't want to do. It is what it is: my campaign for governor is over," Ose wrote.
Dozens of candidates remain in the race, hoping to replace Democratic Governor Gavin Newsom in the September 14 recall election. Mail-in ballots began going out to registered voters in the state on Monday.