كتب : Megan Detrie
The German international was accused of punting a water bottle into the Old Trafford stands after being hit in the face by Cristiano Ronaldo's shot during the game.
"Police have received one complaint in relation to an allegation. Officers are investigating and inquiries are ongoing," a police spokesman was quoted as saying by BBC Sport.
This would not be the first outburst during the highly charged matches between Manchester United and Arsenal.
In 2003, Arsenal defender Martin Keown was fined £5,000 after fighting with Manchester United striker Ruud van Nistelrooy during a 0-0 draw.