Boro coach Leo Percovich has also been charged, along with Blues' head of performance Sean Rush.
The Uruguayan took to Facebook this week to deny throwing a punch in the 87th-minute incident, when referee Andy Woolmer initially waved play on with Boro midfielder Marcus Tavernier down with a head injury, then stopped it before Birmingham found the net. It prompted a melee involving players from both sides.
“I didn’t throw any punches as was said,” insisted Percovich.
After the game, Birmingham manager Pep Clotet accused Boro's bench of “storming the pitch”.
“After I watched the interview with Mr Clotet, the, Birmingham City manager, after the game I noticed he mentioned my person, with a misinformation,” wrote Percovich. “I feel wronged to have anything untrue said about me.
“Let me be clear, I didn’t even raise one hand.
“I was trying to protect my player, as is always my number one priority.”
Percovich and Rush were both sent off in the 1-1 draw.
The clubs are charged with “failing to ensure their officials and/or players conducted themselves in an orderly fashion and/or refrained from provocative behaviour”, the coaches with improper conduct.
All have until Tuesday to respond.