The 27-year-old was detained by the local authorities on the island of Mykonos. It followed a clash between two groups of tourists with police called to the scene to investigate. According to the reports in the Greek press, Maguire was verbally abusive to one of the officers and then hit him.
He is reported to be cooperating with the relevant authorities, and Manchester United are said to be aware of the incident but have declined to comment further at this stage.
Maguire is on vacation in Greece after Manchester Uniteds defeat to Sevilla in their Europa League semi-final last Sunday. Mykonos is a popular destination for Premier League footballers, and Greece has attracted a lot of British visitors this year, because it is one country UK citizens do not have to quarantine themselves after returning from abroad.
Maguires teammates Marcus Rashford and Jesse Lingard are also on holiday in Greece.
On his arrival in the island, Maguire posed for selfies with fans whilst images appeared on social media of him mixing with other people in a local bar. He is also reported to have been serenaded with chants as he walked through the streets.
The English international joined United last summer for 85 million from Leicester City, a record fee for an English defender. He inherited the captaincy from Ashley Young in January, when the wing back moved to Serie A side Inter Milan.
He played more minutes for United than any other player for any club in the top leagues in Europe last season and helped them get back to the Champions League with a third-placed finish.
However, the club finished the campaign empty handed. The Sevilla defeat was their third semi-final loss in a cup competition last season.