It is alleged his behaviour on the field of play at the end of the Premier League fixture amounts to improper conduct and he has until 6pm on 8 March to provide a response.
Hodges has been with Bournemouth since 2012, having previously worked for their opponents last Saturday.
Manchester City won the game 1-0 to keep their title challenge on track but Bournemouth produced a battling display - pleasing manager Eddie Howe with the way they responded to a 5-1 loss to Arsenal last week.