Scunthorpe charged by FA
Veteran Iron striker Steve Torpey was also sent off for violent conduct after confronting Coppinger.
Torpey later issued an apology, with manager Brian Laws stating that the front-man's future at the club may be in doubt.
Both clubs have been charged under FA Rule E20(a) - failing to ensure that its players conducted themselves in an orderly fashion.
United and Rovers have until February 7 to answer the charge.