Dayton had been speaking for about 45 minutes at the state capital when the incident occurred.
Further details were not immediately available, but his son, Eric, tweeted a short time later that his father was "doing great."
In a statement, the governor's chief of staff said that Dayton "quickly recovered" after fainting.
"Tonight, Governor Dayton briefly fainted after speaking for about 40 minutes. He quickly recovered, walked out of the Capitol, and returned home," Chief of Staff Jaime Tincher said.
"EMTs joined the Governor there, and performed a routine check. He is now spending time with his son and grandson."