Pringle exited Sunday's win over the Texans with a calf injury in the first half after catching one pass for 11 yards. In his first season with the Bears, the five-year NFL veteran has two receptions for 33 yards.
Pringle must miss a minimum of four games, which means he won't be eligible to play until Oct. 30 against the Cowboys in Dallas.
Thomas was elevated from the practice squad to the active roster last Saturday and started Sunday's game versus the Texans, recording five tackles.
Thomas originally signed with the Bears March 1 after spending his first seven NFL seasons with the Packers (2015-17), Cowboys (2018-20), Texans (2021) and Ravens (2021). He arrived in Chicago having appeared in 89 games with 16 starts, registering 218 tackles, 12 tackles-for-loss, 1.5 sacks, one interception, 10 pass breakups, two forced fumbles and one fumble recovery.
Last season, Thomas played in five games with the Texans before being released Oct. 16. He then joined the Ravens and appeared in two contests.