The 30-year-old is alleged to have been involved in a crash which damaged a number of vehicles on Saturday morning - the same day that the Black Cats went down 2-0 at home to Preston North End.
A "full investigation" has now been launched by Sunderland, with Gibson - currently nursing a hamstring injury that has ruled him out of action since New Year's Day - said to be fighting for his future.
"Sunderland AFC has suspended Darron Gibson with immediate effect, after the player was charged with driving with excess alcohol on Saturday 17 March," a club statement read. "The football club has commenced a full investigation into the matter."
Chief executive Martin Bain added: "We expect the highest standard of behaviour from our players and should any individual fall short of those standards then robust action must be taken."
Former Manchester United and Everton ace Gibson has featured 15 times in the second tier this term.