According to The Sun newspaper, 29-year-old Olesen allegedly molested a sleeping woman before urinating in the aisle and then getting involved in an abusive tirade with crew on a British Airways flight from Memphis where he had been competing in the St Jude Invitational last weekend.
Olesen, a member of the 2019 European Ryder Cup team and a five-time champion on the European Tour, needed to be calmed down by fellow player Ian Poulter.
London's Metropolitan Police said a 29-year-old man was arrested on suspicion of sexual assault, being drunk on board an aircraft and failing to comply with the orders of cabin crew.
A spokesman said: "He was taken into custody and subsequently released under investigation".
Poulter's agent Paul Dunkley told The Sun that the English star had helped to calm a "slightly intoxicated" passenger, adding: "He (Poulter) then went to sleep and the first he knew of anything else was when the police were waiting at Heathrow."
A European Tour spokesperson told the Daily Telegraph: "This is an active police matter and therefore we have no comment."