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 “cooperating 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.”
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.
Two other Britons were also detained.
“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.”
Information from Reuters was used in this report.