Hawk, a five-year linebacker who amassed a team-leading 111 tackles last season, was scheduled to make $10 million in 2011.
"The business side of the game is driving this decision, Executive Vice President, General Manager and Director of Football Operations Ted Thompson told the team's website (packers.com).
"We're hopeful that we can continue to work with A.J. to have him be a part of our team in the future."
(Writing by Jahmal Corner in Los Angeles; Editing by Patrick Johnston)