The move comes one week after Ryan sustained a torn ACL during practice.
Ryan was slated to start next to Blake Martinez at inside linebacker this season. Oren Burks and Ahmad Thomas were considered as possible replacements for Ryan, according to Packers defensive coordinator Mike Pettine.
The 26-year-old Ryan quickly clutched at his knee and screamed in pain last week as teammates gathered around him, per Michael Cohen of The Athletic.
Ryan started 12 of the 15 games in which he played last season and recorded 81 tackles, a sack and a forced fumble. He collected 206 tackles and one sack in 43 career games since being selected by the Packers in the fourth round of the 2015 NFL Draft.
Also on Monday, the Packers signed running back Akeem Judd, released guard Ethan Cooper and placed rookie linebacker C.J. Johnson on injured reserve with an ailing hamstring.
Judd, who is listed at 5-foot-11 and 225 pounds, spent part of last season on the practice squad of the New York Jets before being released on May 4. He was an undrafted free agent out of Mississippi.