Probe initiated after players are targeted in Bank Holiday weekend deciders
Sheffield Wednesday's Championship game with Crystal Palace on Sunday ended with a pitch invasion that saw visiting player Clint Hill allegedly assaulted several times as he tried to get down the tunnel.
Seven fans were arrested at Kenilworth Road as missiles were thrown at not only the York team but also the police and stewards.
The FA, who are already looking into allegations from Leeds United that three of their players were assaulted during a pitch invasion at Carlisle United in February, have confirmed that the clubs involved will be written to along with the respective local authorities.
An FA spokesman said: "The FA does not condone disorder either outside or inside football stadia and, thankfully, such problems remain infrequent in the modern game.
"However, any individuals identified as having taken part in any form of disorder should be dealt with appropriately by the authorities and issued with football banning orders as they simply have no place in our game."
Luton supporters invaded the pitch after their team lost 1-0 to York in the play-off semi-final second leg for a 2-0 aggregate exit.
Six of the seven arrested have been bailed with a seventh person, a Scandinavian man, still waiting to hear whether he will be taken to court.
Stewards and police had to help York's players to escape to the dressing rooms, via the away end, as missiles were thrown.
The violence then spilled over to nearby Dunstable Road, where a smaller number of fans attacked police with mops and brooms taken from outside a DIY store. A number of police officers received minor injuries.
Luton chairman Nick Owen described the clashes as "absolutely dreadful".
He added: "One or two of our fans have let the club down. To be honest, it is shattering."
Meanwhile, a spokesman for South Yorkshire Police said arrests were made at Hillsborough for public order and assault offences.
Wednesday supporters were also involved in disorder outside the ground just after the game, when police vehicles and nearby property was damaged.
Fans of both the Owls and Palace had invaded the pitch after the final whistle blew to signal that the London side had avoided relegation at the expense of their hosts.
Television footage showed Hill requiring the protection of stewards en route for the tunnel and the Palace defender later alleged he had been struck several times.
The trouble at Wednesday and Luton came a little under three months on from Leeds manager Simon Grayson alleging three of his players had been struck during a pitch invasion by Carlisle fans celebrating reaching Wembley in the Johnstone's Paint Trophy. Shane Lowry, Robert Snodgrass and one unnamed player are believed to have been the players involved.
The FA launched an investigation but, as yet, have not released any findings.
It is understood they were keen not to heighten tension ahead of last month's League One meeting between the two clubs, which passed off peacefully as Leeds triumphed 3-1.