Video from on board the plane shows Tyson throwing punches at a man over his seat.
A second clip shows the man with blood on his head.
Tyson is said to have got off the plane moments later while the man involved is believed to have needed medical attention and went to the police to report the incident.
"Unfortunately, Mr. Tyson had an incident on a flight with an aggressive passenger who began harassing him," Tyson's team said in a statement later on Friday.
"And threw a water bottle at him while he was in his seat."
San Francisco Police told TMZ that two men were detained following the incident and, after one was treated for his injuries, he "provided minimal details of the incident and refused to cooperate further with the police investigation."
Footage of the altercation has reportedly been forwarded it to the San Mateo County Sheriff's Office.
Tyson was one of the best fighters of all time and won 50 of his 58 fights, reigning as undisputed heavyweight champion of the world from 1987 to 1990.
His life has been mired in controversy, and Tyson was jailed in 1992 for rape.
He regained a heavyweight title following his release after three years, but found himself in the spotlight for the wrong reasons again when he bit off part of Evander Holyfield's ear during a title fight.
He would later admit to having a cocaine addiction after being caught driving on drugs.
