Van Persie was lying on the floor in the second half of Sunday's 1-1 draw with Swansea City and Williams, apparently attempting to clear the ball, hammered it into the back of the striker's head after the whistle had gone.
However, Ferguson felt Williams deliberately tried to strike van Persie with the ball and says that his striker could have died as a result.
A melee then ensued, but under Football Association rules Williams cannot be punished for the controversial moment if the yellow card he was shown by referee Michael Oliver was for the kick, rather than for the pushing and shoving that followed.
Ferguson believes the Swansea skipper deserves to be suspended for a lengthy spell as a result of the incident.
"Robin van Persie is lucky to be alive," he told the BBC. "It was a disgraceful act from their player today and he should be banned by the FA. Robin could have had a broken neck."
Ferguson added on Sky Sports: "He (Van Persie) could have been killed - I think the FA has got to look into it.
"I think irrespective of having a yellow card, he should be banned for a long time because it was the most dangerous thing I have seen on a football field for many, many years.
"Absolutely deliberate. The whistle has gone, the game has stopped and he has done that right in front of the referee.
"A foot from the player (Van Persie) - he could have really killed the lad. It was a disgraceful act by the player and he should be banned for a long, long time."
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."