The 20-year-old has been arrested on suspicion of rape and assault following allegations made by his girlfriend in a series of social media posts, including images and a voice note.
Man United have suspended the England international, who will not be allowed to train with the team or feature in matches "until further notice".
Greater Manchester Police confirmed that they have made an arrest on Sunday, with the man "in his 20s" placed in custody, where he remained overnight for questioning.
The Red Devils have now made Greenwood merchandise unavailable to purchase on their online store.
Man United will be back in action against Championship side Middlesbrough in the fourth round of the FA Cup on Friday evening, but Greenwood will not be involved for Ralf Rangnick's side. body check tags ::