"And thanks to the GOAT [greatest of all time], Dr. ElAttrache, and his staff for starting me on the road to recovery."
Rodgers sustained the left leg injury in the first quarter of the Jets' 22-16 win over the Buffalo Bills on Monday in East Rutherford, N.J.
The veteran quarterback, who considered retirement last off-season, joined the Jets through an April trade from the Green Bay Packers. He is signed through 2024, but his contract includes an option in 2025.
Jets coach Robert Saleh said Wednesday he expects Rodgers to return next season.
"I'm completely heartbroken and moving through all of the emotions, but deeply touched and humbled by the support and love," Rodgers wrote Wednesday on Instagram. "Please keep me in your thoughts and prayers as I begin the healing process."
"The night is darkest before the dawn. And I shall rise yet again. Proud of my guys, 1-0."
Zach Wilson will be the Jets' starting quarterback in Week 2. The Jets (1-0) will face the Dallas Cowboys (0-1) at 4:25 p.m. EDT Sunday in Arlington, Texas.