Manchester United manager Alex Ferguson claimed the Dutchman was blasted "deliberately" in the head with the ball by Swansea's Ashley Williams.
Van Persie was on the ground after being fouled by Nathan Dyer on the edge of the box when Williams hacked at a loose ball which cannoned into the striker's head from less than a metre away.
The striker reacted angrily, prompting a short melee with pushing and shoving from opposing players before Van Persie and Williams were both booked.
"He could have been killed. I think the FA has got to look into it - irrespective of him getting a yellow card, he should be banned for a long time, because that was one of the most dangerous things I have seen on a football pitch in a long time. Absolutely deliberate.
"The whistle had gone, the game stopped and he has done that right in front of the referee. He could really have killed the lad."
Williams played down the incident, saying it was an accident.
"I just cleared the ball with frustration and unfortunately it hit him in the head and he got a bit angry about it," he said. Everything got a bit heated but it was all right in the end." - Reuters