Spokesman Greg Aiello told The Associated Press the league is "in the process of reviewing all the facts" and Bears spokesman Scott Hagel said the team is doing the same thing.
"Right now, we're monitoring it," Hagel said.
Milwaukee's WITI-TV aired video in which Collins is seen yelling at a fan as he left the field. Collins then appears to throw his mouthpiece into the stands. According to the station's report, Collins said the fan spit on him and used a racial slur.
WITI said Collins apologized for "losing his cool."
Packers coach Mike McCarthy said he hadn't seen the video but had been briefed on the situation by the Packers' security department.
"I understand Nick's story, as far as what happened and what our security people that were there [said]," McCarthy told reporters in Green Bay on Tuesday. "And I support Nick 100 percent."
Still, McCarthy said players would be wise to avoid such confrontations.
"You don't want to get into interaction, particularly with opposing fans," McCarthy said. "It is an emotional time, particularly after a game. I think it's something we can all learn from."
Collins, a veteran safety who has been selected to two straight Pro Bowls, may have been frustrated after being caught in the middle of two penalties that helped turn the game in the Bears' favor.
With the score tied at 17 and the Bears driving in the final minutes of the game, Collins intercepted a pass from Chicago quarterback Jay Cutler. But the play was wiped out by a pass interference penalty on rookie safety Morgan Burnett, putting the Bears in position to kick the game-winning field goal.
"I saw that yellow flag down, and you're like, 'Aw, come on, man,'" Collins said after the game. "It happens. It's just part of the game."
Earlier in the quarter, Collins was called for unnecessary roughness on Bears running back Matt Forte after a 15-yard reception, allowing the Bears to continue a drive for a game-tying field goal.