Brown, 37, suffered a shoulder injury in practice on Monday and was held out of team activities for the rest of the week.
The 15th-year veteran was ruled out for Sunday's season opener against the Baltimore Ravens on Friday, but his injured reserve status opens a roster spot for the Jets.
Brown's is just the latest injury for a New York team trying to escape the AFC East cellar.
Brown was signed to a two-year, $22million contract last month after tackle Mekhi Becton was shut down for the season with a fractured right kneecap.
Jets starting quarterback Zach Wilson will miss at least three games as he recovers from surgery to repair a non-contact knee injury suffered in a preseason game. Joe Flacco will start under center in the meantime.