The Wales centre-back struck the prone Van Persie in the back of the head with the ball during the second half of the match, sparking a furious reaction from the Dutchman that culminated in bookings for both players.
Swansea top scorer Michu had earlier cancelled out Patrice Evra’s opener for United to prevent Ferguson’s men from restoring their six-point advantage over second-place Manchester City at the English Premier League summit.
“Robin van Persie is lucky to be alive,” said Ferguson.
“It was a disgraceful act from their player today and he should be banned by the FA (Football Association). Robin could have had a broken neck.
“It was one of the most dangerous things I’ve seen on a football pitch in many, many years. It was absolutely deliberate, and right in front of the referee.”
Williams claimed it had been an accident, telling Sky Sports: “I just cleared the ball with frustration and unfortunately it hit him in the head and he got a bit angry about it.”
Swansea threatened first in the match, Michu firing off-target after out-pacing the returning Nemanja Vidic, before Wayne Rooney and Ashley Young tested fit-again Swansea goalkeeper Michel Vorm at the other end.
United took the lead in the 16th minute, with Evra getting in front of his marker to dispatch Van Persie’s corner and claim his third goal – all headers – of the season.
Michu headed over from Nathan Dyer’s cross, but it did not take long for the Spaniard to find the net.
In the 29th minute, Wayne Routledge’s cute pass freed Jonathan de Guzman and when his shot was parried by David de Gea, Michu followed up from close range to claim his 13th league goal of the campaign.
Vorm saved from Rooney again before half-time, while at the interval, Ferguson harangued referee Michael Olivier for failing to penalise Chico Flores for a challenge on van Persie prior to Swansea’s equaliser.
De Gea thwarted Kemy Agustien and Routledge early in the second period, before Van Persie hooked a superb volley onto the top of the Swansea crossbar from a left-wing Rooney cross.
Michael Carrick then hit the bar from a corner, while both Van Persie and Ashley Young were thwarted by some last-ditch defensive blocks, but Williams’s clash with the former Arsenal striker was to prove the biggest talking point.
It was United’s first draw of the season in all competitions and leaves them four points above City ahead of the home game with Newcastle United on Wednesday.