McCown sustained the injury after being knocked to the ground by outside linebacker Shane Ray during the third quarter of Sunday's 23-0 loss to the Denver Broncos, ending what had been his best season during his 15-year NFL career.
"It's big for (McCown), and it's big for us," coach Todd Bowles said of the injury's impact for the Jets (5-8), per NJ.com. "He was the leader all year offensively. For him to go down this late in the season, I feel sorry for Josh. He was having a very good year. He meant a lot. The leadership meant a lot, from the time he walked in the door."
Signed to a one-year, $6 million contract in the offseason, McCown was emotional when discussing the injury on Sunday.
"When I threw, I got hit and kind of got rolled up," the 38-year-old McCown said. "He kind of rolled over me and either a knee or a foot or something of his caught my hand and it bent funny. I knew when it happened something wasn't right."
McCown was selected as the AFC Offensive Player of the Week last week and took every snap this season prior to his injury. He set career highs in completions (267), passing yards (2,926) and touchdowns (18) and also matched a personal best with 13 starts, set originally in 2004.