The 33-year-old midfielder has had a series of calf problems throughout his career and had to come off in the first half of the victory over Hartlepool due to an injury in the same area.
Thirlwell could be joined on the sidelines by utility player Chris Chantler, who was also substituted against Pools after suffering a knock on his ankle.
Veteran forward Danny Cadamarteri is not expected to return until January due to a calf injury he picked up in training.
However, there is better news elsewhere for the Cumbrians as James Berrett nears full fitness.
The midfielder has been missing due to a groin injury but manager Greg Abbott admits he is closing in on a return.