"With A.J., the business side of the game is driving this decision," general manager Ted Thompson said in a statement. "We're hopeful that we can continue to work with A.J. to have him be a part of our team in the future."
Hawk, drafted fifth overall in 2006, had 111 tackles in 2010 after finishing with less than 90 tackles in each of the previous two seasons. Hawk also had three interceptions this season and has played in all 80 regular-season games since 2006 with 77 starts.
Lee has spent six seasons with Green Bay after being drafted in the fifth round by Miami in 2003. His best season came in 2007, when he caught 48 passes for 575 yards and six touchdowns.
"We want to thank Donald for all of his contributions to the Packers and for being a good teammate throughout his career in Green Bay," Thompson said in the statement. "He has been a professional and we wish him well in the future."
Lee was set to earn $2.2 million in 2011, while Martin was slated to make $750,000.
Information from The Associated Press contributed to this report.