The injury happened during a red zone period in a joint practice between the Jets and Green Bay Packers at the Packers' facility. Several players took knees and the practice fell ominously quiet as medical personnel tended to Lawson.
Safety Zane Lewis also suffered a season-ending injury during the joint practice as the Jets said he tore a patella tendon and sprained an MCL.
Lawson's season-ending injury is a huge blow to the Jets, who were counting on him to be their primary edge-rushing threat in their new 4-3 front. He had been dominant in training-camp practices.
Lawson struck a hopeful tone while addressing the injury news on Instagram.
The loss of Lawson will force the Jets to retool their defensive line under new head coach Robert Saleh, who spent the past four seasons as the San Francisco 49ers' defensive coordinator.
Saleh is no stranger to dealing with injuries and still fielding a strong defense. The 49ers ranked No. 5 in total yards allowed last season despite the losses of Nick Bosa, Solomon Thomas, Dee Ford, Richard Sherman and Ezekiel Ansah due to injuries.
Bryce Huff, an undrafted free agent last year out of Memphis, is the favorite to get an opportunity to replace Lawson as a primary pass-rusher for the Jets.
The Jets signed Lawson to a three-year, $45 million contract in March. He spent his first four seasons with the Cincinnati Bengals.
Lawson has a history of major injuries. He tore his left ACL at Auburn in 2014, and he tore his right ACL with the Bengals in 2018.
The Associated Press contributed to this report.