Maguire was detained after allegedly assaulting officers who were called in to break up a brawl between two groups of tourists.
United have confirmed the England international defender is "co-operating with authorities" and they have been in contact with him.
The club issued a statement on Friday morning that read: "The club is 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."
Local police said three British nationals face charges of verbally abusing and using physical violence against police, as well as attempted bribery.
The three men allegedly abused and punched one of the policemen who was attempting to break up the quarrel, resisted arrest, and subsequently attacked officers outside the police station, police said, without naming Maguire.
A police statement said one of the three arrested men tried to offer police money to avoid being taken into custody. Syros is the administrative center of the Cyclades islands, where Mykonos is.
Maguire has been on holiday on Mykonos since United's season ended with a 2-1 defeat to Sevilla in the Europa League semifinals on Sunday.
"The soccer player was verbally abusive to an officer and then hit him," a police official said. "The three were resisting when brought to the Mykonos police station."
Maguire is expected to appear before a prosecutor in a Greek court on Saturday.
Information from Reuters and the AP was used in this report.