The Packers drafted Madison in the fifth round in 2018. Madison, 25, did not report in 2018 and remained on the reserve list all year.
In 2019, he returned but did not play in a game before going on injured reserve with a torn ACL.
Jones signed April 29 as an undrafted free agent out of Prairie View A&M. The Packers claimed John Lovett off waivers Thursday for the H-back role.
The Packers also placed offensive guard Simon Stepaniak and running back Patrick Taylor on the non-football injury list. They put linebacker Curtis Bolton and offensive tackle Yosuah Nijman on the physically unable to perform list.