He also got in a few punches. Beckham followed the exchange by shouting toward the field. Rookie running back Saquon Barkley walked over to the wide receiver and attempted to calm him down, before Beckham went to the bench.
The fan altercation came just after Barkley scored a touchdown for the Giants. Beckham walked into the locker room -- while the Giants' offense was still on the field -- just before the first half clock ran out.
"I was trying to get myself going," Beckham told reporters. "I feel like some of those plays right after I was getting myself going was some of my best stuff. I was trying to get myself fired up, I did that, and it helped me. There was a lot of things that had me fired up. Like I said, it helped me bring out the energy, I don't know a way around it but to get myself going."
Beckham previously got into a fight with a kicking net during a Giants game in 2016 against the Washington Redskins. He tried to make up for that vicious exchange by later hugging a kicking net and proposing to another net after scoring a touchdown.
Beckham had six catches for 44 yards in Thursday's loss. The three-time Pro Bowl selection has 506 yards and one score on 45 receptions this season.
"They definitely had a plan to slow down Odell," Giants quarterback Eli Manning said. "A lot of teams do. We could still run our offense. We have guys that get open and make plays. We have to do a better job of executing our offense. That is what it is about. Trying to move the ball."
Giants coach Pat Shurmur said he didn't see Beckham head-butting the net but that the wide receiver "can't do that."
The Giants face the Falcons at 8:15 p.m. on Oct. 22 in Atlanta.