Smith will be out six to 10 weeks for the injury, which happened as a result of a dispute with linebacker IK Enemkpali, ESPN reports.
Enemkpali reportedly bought a $600 plane ticket so Smith could attend his charity football camp in Pflugerville, Texas, on July 1, sources told ESPN.
But Smith never showed, claiming a close friend died in a motorcycle accident just before the event, according to ESPN.
Enemkpali then demanded that Smith reimburse him the money. When Enemkpali confronted him on Tuesday, the two got into an argument and the linebacker ended up punching the quarterback in the jaw, according to multiple reports.
Enemkpali, a free agent who was drafted by the Jets in 2014, was let go over the incident.
"It had nothing to do with football. It was something very childish," head coach Todd Bowles said in a statement later Tuesday. "He got cold-cocked, sucker punched, whatever you want to call it, in the jaw. He has a broken jaw, fractured jaw.
"The team knows it's something we don't tolerate, something we can't stand. You don't walk up to a man and punch him in the face."
Enemkpali has since apologized for his behavior, telling the Associated Press in a statement: "Geno and I let our frustration get the best of us, but I should have just walked away from the situation.
"I deeply regret and apologize for my actions. It was never my intention to harm anyone. I appreciate the opportunity I had with the Jets."
As for Smith, he's not going to let the injury stop him. The quarterback posted a picture to Instagram on Tuesday with the caption, "ILL BE BACK!"
Smith will likely be out until October.