Maguire appeared in a photo on Friday when he was taken into custody by police on the island of Syros, which is a neighboring island to Mykonos.
He has "cooperated" with Greek authorities, United said in a brief statement, after the incident.
The Greek TV channel states that Maguire's brother and a friend were also arrested.
Local police say three British citizens are accused of verbal abuse and use of physical force against police as well as attempted bribery, after police intervened in a fight between two groups. The three men are said to have beaten a police officer who tried to avert the quarrel, the police say without naming the people.
United players are on holiday after losing to Sevilla in the Europa League semi-final on Sunday.
The 27-year-old Maguire is the world's most expensive defender, after the transfer from Leicester to United in a deal worth about SEK 800 million.