The City boss is set to face the charge in the aftermath of the 'Battle of the Bank', following him being sent to the stands for his role in the altercation.
He was sent to the stands rather than being red carded, a fate suffered by Aaron Brown, and substitutes Ian Pearce and Barry Richardson.
The initial problem was caused by a mistimed challenge by Brown on the Robins player Theo Lewis, and the reaction of the Cheltenham players and management.
Sutton has been charged under FA rule E3 – improper conduct.
He now has until 6pm on Tuesday to eitehr contest the charge, or admit his guilt.