Both clubs have been charged with breaches of FA Rule E22a for failing to ensure that their players conducted themselves in an orderly fashion.
The charges follow the 'mass brawl' during last Sunday's match at the Riverside. Duncan Ferguson initially challenged Boro keeper Mark Schwarzer, after the Aussie had dropped a cross, and every outfield player appeared to join in.
The two clubs have until Wednesday 2nd February to respond to the charges.