Van Persie was lying on the ground when Williams kicked the ball from a couple of yards away as the referee blew the whistle for a foul.
Ferguson felt Van Persie was fortunate to escape serious injury.
“Robin van Persie is lucky to be alive. It was a disgraceful act from their player,” Ferguson told BBC Sport.
“He should be banned by the FA. Robin could have had a broken neck.”
The United manager said Williams, 28, had deliberately aimed the ball at Van Persie, who reacted furiously – both players were cautioned by referee Michael Oliver.
Ferguson added on Sky Sports: “With the Van Persie situation, you can clearly see that he could have been killed.
“He should be banned for a long time because that was the most dangerous thing I’ve seen on a football field for many years.
“It was absolutely deliberate. The whistle has gone, the game has stopped and he has done that right in front of the referee, he could have killed the lad.
“It was a disgraceful act by the player, he should be banned for a long time.”
Williams denied he had hit Van Persie intentionally.
Williams on Van Persie incident
“I’ve seen it on the TV and that’s his [Ferguson’s] opinion,” said Williams.
“Everyone’s going to have their own opinion but, from my point of view, I tried to apologise on the pitch but it all flared up.
“I just kicked the ball in frustration and obviously not trying to hit him square on the head.
“I understand exactly why he’s angry. I’d be the same if the ball hit me on the head at that pace.”
United striker Wayne Rooney tried to play the incident down.
“I think it’s one of those things,” he said. “The whistle’s gone, the defender has gone to clear and it’s hit him in the head. I think probably the right decision from the referee.”
United led the Premier League by six points going into the weekend’s fixtures but, after the draw with Swansea and rivals Manchester City’s win over Reading, that advantage has been cut to four points.
“It should have been six. That’s the disappointment,” added Ferguson.
“We absolutely battered Swansea [in the second half].
“In the second half it was a marvellous performance by us and we were unlucky not to win it. We struck the bar twice and had some great chances.
“If there is a criticism then maybe it is that we were wasteful with the chances and we have to hold out hand up to that.”
The United manager was angry that referee Michael Oliver, 27, did not disallow Swansea’s equaliser for a foul by Chico on Van Persie during the build-up to the goal.
“It really it should have been a foul for us when the defender fouled Van Persie but the referee has had one of those games,” said Ferguson.
“I know he is a young referee but dear me what a performance that was.”