Hart clashed foreheads with Hull substitute Boyd during a furious exchange in Man City's 2-0 Barclays Premier League win at the KC Stadium on Saturday.
The England international was booked by referee Lee Mason for his involvement and the FA has confirmed that - in line with the governing body's own rules - it considers the goalkeeper to have been dealt with.
The flashpoint occurred when Boyd was denied a penalty after claiming to have been fouled by Hart.
It has also not yet been decided whether Man City captain Vincent Kompany could face further disciplinary action for his reaction to his sending-off in the fiery contest.