Pace was injured in a preseason game against the Washington Redskins on Friday and will undergo surgery on Monday.
"I'll probably definitely miss the first game, it's safe to say that," Pace told the Jets website (newyorkjets.com).
"Beyond that I don't really have an idea. Hopefully it'll still be a somewhat speedy recovery."
The injury is yet another setback for the Jets' defense, already missing All-Pro cornerback Darrelle Revis, who is embroiled in a contract dispute.
Pace has seven years of experience in the NFL and has played a good contributing role to the Jets for the last two years.
The Jets open the season at home to the Baltimore Ravens on September 13.
(Reporting by Jahmal Corner in Los Angeles; Editing by John O'Brien)