Adams has a toe injury and Burgess a hamstring injury.
Adams, 25, has played eight games this season. He has seen action on 130 defensive snaps and 71 on special teams.
Burgess, 26, has played four games and made three tackles. He has seen action on 51 special teams snaps.
The Packers also claimed defensive tackle Anthony Rush off waivers from the Bears, Field Yates of ESPN reports.
Rush appeared in four games for the Seahawks this season, making six tackles and half a sack.