The video was tweeted by punter Steve Weatherford and contains some unsavory language. It shows Pierre-Paul carrying Amukamara, a cornerback, on his shoulder and tossing him head-first into one of the tubs players use to relieve injuries.
Amukamara did not struggle while being carried, but appears upset when he emerges from the tub.
Pierre-Paul then uses insensitive and obscene language and high-fives a teammate.
"I'm learning about that today," Coughlin said in a conference call with reporters Sunday afternoon. "I really didn't have any information about that until maybe an hour before this conference call. I am going to look into it and talk to the parties involved.
"There may have ... as I'm understanding it, there were some parts of it that were inappropriate. In no way is anything that occurs within this family or within our group should that be a part of any social media aspect. So I am going to address that strongly because I spent a little time on that this preseason. I will look into that further."
Weatherford apologized on Sunday for posting the video.
"I want to apologize to the fans... The video I posted was distasteful," Weatherford tweeted. "Our team is a family, and we love each other. I am sorry to the fans."
NFL spokesman Greg Aiello told nbcsports.com's Pro Football Talk the league regards the incident as a "club matter."
Amukamara, 23, was the target of rookie hazing last season. He said had his tie and dress shirt cut before a road trip and landed in the cold tub eight times last year.
"Yeah, um, well, I mean, I just don't get it. I don't understand the rules," Amukamara told the Newark Star-Ledger on Saturday night after the Giants beat the Jets, 26-3. "I mean, I'm not a rookie anymore, so I don't know why I'm getting thrown in the tub. I know it's all love.
"Yeah, no one ever likes it, especially when it's you versus eight and no one's helping you. But it doesn't mess up our team morale or anything.
"I don't think I did [anything to provoke it]. I don't think I did. Ask them."
After Amukamara landed in the ice tub, a player tells Amukamara to "stand up for yourself."
According to the Star-Ledger report, players have been trying to get Amukamara to "develop an edge."
Amukamara said that the veterans have told him that he has three more regular-season games to complete before he's considered "one of them."
-- The Sports Xchange