In a statement, league officials said Collins "violently and unnecessarily struck a defenseless receiver" in the neck and head area with his helmet during Sunday night's game at Lambeau Field and called it a "flagrant violation of player safety rules."
NFL executive vice president of football operations Ray Anderson told Collins that further offenses "will result in an escalation of fines up to and including suspension."
The NFL is cracking down on illegal hits, and players who violate the rules are subject to increased fines or even suspensions.
Collins went helmet-to-helmet with Williams after an incompletion in the third quarter of the Packers' 45-7 victory over the Cowboys on Sunday night. Collins was flagged for unnecessary roughness.
Williams said after the game that he didn't think NFL Commissioner Roger Goodell should punish Collins for the hit.
"Commissioner Goodell, don't fine the guy," Williams said. "It wasn't that bad of a deal, he shouldn't get fined. It was a football play, a football player making a football play. No injury, no harm."
Packers coach Mike McCarthy said he spoke to side judge Rick Patterson immediately after the play.
"It was a bang-bang play and I felt that really when I saw the replay on the Jumbotron, it looked like Nick hit Roy in the back and came up to the helmet," McCarthy said Monday. "I understand why Rick threw the flag and we actually talked about the mechanics of it. That's a tough call.
"I think the referees are doing a very good job with the awareness of player safety, but I was standing right there and I can see what Nick Collins saw, too. The ball was in the air and he was trying to run through the proper target line and I think he hit Roy in the top of the pads and went up into the helmet."
Packers defensive coordinator Dom Capers says that while players are taught to play within the rules, it can be difficult to avoid a hit that is considered illegal when trying to hit a moving target.
"It's such a fine line, because you want guys to play aggressively within the rules," Capers said. "That target changes sometimes a little bit, and when you're out there going full speed and that target changes a little bit, sometimes you might end up 2 or 3 inches from where you aimed to begin with."
The NFL did not hand out any discipline for the hit that gave Indianapolis wide receiver Austin Collie a concussion in Philadelphia on Sunday.
Collie was hit by safety Quintin Mikell, then took a shot to the helmet from fellow safety Kurt Coleman's helmet in the second quarter. Collie briefly lost consciousness and was taken off the field by stretcher.
Coleman was penalized for unnecessary roughness.
The NFL said because the helmet-to-helmet contact was a result of Collie being driven toward Coleman by Mikell's legal hit, there will be no fine. The league said game officials have been instructed to err on the side of player safety, and when in doubt, "penalize in situations such as this for unnecessary roughness."