The NFL, announcing the suspension on Thursday, said Pace will be eligible to return after the Jets' Oct. 4 game against the New Orleans Saints.
In a statement released by the Jets, Pace said the suspension stemmed from his use of an over-the-counter dietary supplement -- which he did not identify -- that contained a substance he did not know violated the policy.
"I am responsible for what I put into my body and I should have paid closer attention to the League's guidelines. I regret that this has happened and apologize to my teammates, the entire Jets organization as well as the fans," Pace said. "Hopefully, this does not distract from our ultimate goal of winning the Super Bowl."
The Jets said they respected the league's decision and looked forward to Pace's return for their Monday night game against the Miami Dolphins in Week 5.
Pace finished second on the team last season with a career-high seven sacks, and added 67 tackles, five forced fumbles and four fumble recoveries. Pace signed a six-year, $42 million deal with New York last offseason that included a $20 million signing bonus. He spent his first five NFL seasons with the Arizona Cardinals, who selected him with the 18th pick in the 2003 draft.
Second-year linebacker Vernon Gholston, who had a disappointing rookie season, is expected to fill in at one of the outside linebacker positions, opposite starter Bryan Thomas. Ryan repeatedly said he was excited at the progress made by the former Ohio State star during minicamp and offseason workouts. Marques Murrell and Jason Trusnik will also be options to fill in.
Information from The Associated Press was used in this report.