The United manager accused Swansea captain Ashley Williams of deliberately kicking a ball at the striker's head from close range in the Barclays Premier League game at the Liberty Stadium.
With Van Persie falling to the ground after he was fouled on the edge of the area, Williams cleared the ball into the back of the Dutchman's head from close range.
Van Persie reacted angrily and squared up to Williams with referee Michael Oliver electing to book both players.
Ferguson was furious tougher action was not taken by the official and has called on the Football Association to ban the Wales international.
"The Van Persie situation you can clearly see that he could have been killed," Ferguson said on Sky Sports News.
"The FA has got to look into it regardless that he has been given a yellow card. 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 banned for a long time."
He added to BBC Sport: "Robin van Persie is lucky to be alive. It was a disgraceful act from their player.
"He should be banned by the FA. Robin could have had a broken neck."
Swansea manager Michael Laudrup appeared bemused when informed of Ferguson's comments.
He said: "I did not see it at the time as there were a lot of players involved, but I saw it afterwards.
"I don't think he (Ferguson) meant literally killing him.
"Things happen in a game and I am sure Ashley and Van Persie shook hands at the final whistle and we move on.
"When your pulse is on 180 then you can say things during the game you don't mean but then afterwards it is back to normal."
Williams looked to downplay the incident too.
"I tried to clear the ball it hit him on the head," he added. "I was trying to clear the ball.
"He was obviously a bit angry about that. It was a much ado about nothing."
Patrice Evra had given the visitors a 16th-minute lead before Michu equalised just before the half hour mark.
Ferguson was angry with Oliver for not awarding his side a free-kick for what he thought was a foul on Van Persie in the build-up to what was Michu's 13th goal of the season.
"It was foul on van Persie, a clear foul," he said. "The referee had one of those days where we didn't get anything out of him.
"It was a shocking performance. I know he is a young referee but I was disappointed with that performance."
Ferguson was less critical of his players and felt they did more than enough to take claim the three points which would have put them six points clear of rivals Manchester City at the top of the table.
"Thrown two points away really," he added. "We absolutely battered them. It was a great performance in the second half. It is unbelievable we didn't win the match.
"My only criticism is that the final ball at times let us down. No criticism of the performance, it was very good."
United came closest to getting that winner after 78 minutes when Michael Carrick headed onto the bar, but Swansea held on to end a run of two consecutive defeats.
"There is a reason why they are top," Laudrup said. "They have very good players .
"They had the first maybe one or two chances but we came back and I think that was great. In the second half they put us under pressure they really wanted to win. They had a couple of big chances.
"It was fantastic the way we handled everything I'm very pleased. You know up against Van Persie, Rooney and company they will always create chances. Just after the goal at 1-0 they had 10 minutes when if they score a second it would have been very difficult.
"They started a bit better than us, scored the goal and had five to 10-minute period where they could have scored a second which would have made it difficult.
"We equalised and I thought first half was an equal contest, in the second half it was a more open game.
"They had more of the ball and created more chances but I felt it could have gone either way.
"They had more chances but that is normal when playing a side who are top of the table.
"It is a great point for the club and the players. I heard last season there was too much respect shown for United, that was not the case today [Sunday]."
Williams was equally bullish about their performance.
"I think so (we deserved a point), we worked hard," Williams said.
"We lost twice to them last season and we lost the last two so we needed something.
"We had to dig in. You saw how close we are as a team everyone was defending and working hard.
"They are a brilliant team so we are happy with a point."
When told about Ferguson's reaction to the incident, Williams said: "It's his opinion, he's entitled to it. I understand why Van Persie was angry. I've kicked the ball away in frustration, but I wasn't trying to hit him in the head."
Quoted by the Daily Telegraph, he said: "I tried to say sorry, but he wasn't having it. I haven't spoken to him since the game and I didn't shake hands afterwards - but only because I didn't see him. As far as I'm concerned it's no big deal.
"If I had tried to hit him on the head deliberately, I would have missed!
"It's not like I'm going to shoot and hit him square in the head like that."