The 76-year-old is also accused of bringing the game into disrepute, but a statement issued by the Football Association on Thursday did not identify the specific incident for which he is being charged.
Coates attracted controversy earlier this month when he backed manager Mark Hughes' criticism of referee Chris Foy after he failed to punish West Ham's Alex Song for an apparent two-footed challenge on Mame Biram Diouf.
"There does seem to be a bias towards other teams," Coates was quoted as saying at the time. "You always feel that because we have a good crowd that gets behind the team, referees seem to think 'I will show them who's in charge here'.
"Perhaps it's a macho thing."
Coates also alleged defender Ryan Shawcross was receiving unfair treatment from officials, and criticised television pundit John Hartson for comments the former Wales international made regarding a perceived dive by Victor Moses in Stoke's 2-1 win over Swansea City in October.
Coates has until November 24 to appeal the charges.
