United said in a brief statement they were “aware of an alleged incident involving Harry Maguire in Mykonos last night.”
“Contact has been made with Harry, and he is fully co-operating with the Greek authorities.
“At this time we will be making no further comment,” the club added.
A Greek police statement on Friday said that three men aged 27, 28 and 29 had been arrested in Mykonos.
A police officer in Syros, the capital of the island group that includes Mykonos, confirmed to AFP that the suspects are “three British men, including a British football club player” but did not name Maguire.
The police statement said officers responding to an “altercation” had been verbally abused, and one officer had been punched.
A second fight broke out at the local police station where the three men “strenuously resisted (arrest), pushing and striking three officers,” the statement said.
One of the suspects then tried to bribe the officers to hush up the incident, the police said.
The Syros officer said four Mykonos officers had sustained slight injuries in the fracas.
The suspects are accused of assault, resisting arrest, verbally insulting and threatening the arresting officers, and attempted bribery, the police said.
Greek state agency ANA said a fight had broken out between British tourists outside a bar.
The agency identified the suspects as Maguire, his brother and a friend.
ANA said the police had asked the suspects to follow them to the police station in a mini-van but when they arrived, they attempted to flee.
They will appear before a Syros prosecutor later Friday, the local officer said.
Footage from a Mykonos celebrity-watching website believed to be shot on Wednesday, a day before the incident, had shown the England centre-back greeted by a fan in the island capital’s crowded narrow streets.
United’s Europa League season ended Sunday in a 2-1 defeat to Sevilla.
But the club will be back in pre-season training in two weeks and could begin their Premier League campaign in less than a month.
The incident on Mykonos came ahead of a COVID-19 night curfew in nightclubs and restaurants that came into effect Friday.
Eateries and bars on the all-night party island are now supposed to close at midnight, masks are compulsory, and only groups of up to nine people are allowed outside.
But operators complain that patrons leaving their establishments simply congregate on the street.
Greece has registered nearly 8,000 coronavirus cases — over 3,000 of them just this month — and 235 deaths.