The Eagles announced Babin's release in an emailed statement.
A statement attributed to head coach Andy Reid read "We appreciate everything that Jason has given this team over the last couple of years. We wish him all the best as he continues his career. By releasing him today, this gives us an opportunity to give more playing time to some of younger guys in the defensive line rotation."
Babin was 3rd in NFL last year with 18 sacks but this year he's tied for 34th with just 5.5 sacks.
He signed a five-year, $28 million deal last summer after going to his first Pro Bowl with Tennessee following the 2010 season.
Reid made the announcement about Jackson's injury during a Tuesday afternoon news conference.
Jackson left in the first half of Monday night's game against the Carolina Panthers.
Reid said Jackson injured multiple ribs "up high" and was placed on injured reserve.
In other injury news, Reid said running back LeSean McCoy has not progressed in his recovery from a concussion, and quarterback Michael Vick - also suffering from a concussion - has not yet passed the IMPACT test.
T Jason Peters, who had not recovered from his Achilles tear, was also placed on injured reserve.
The Eagles lost to the Panthers 30-22, dropping to a 3-8 record after losing seven straight games.
The Eagles play at Dallas (5-6) on Sunday night.