The 30-year-old sustained the injury on Saturday during his side's 2-1 win at home to Oxford United in League Two.
The experienced forward is due to undergo surgery on Thursday before starting his rehabilitation.
"Stephen has ruptured his Achilles tendon," Carlisle physio Neil Dalton told the official club website. "He will now have surgery on Thursday evening with our surgeon and will obviously go into a rehabilitation process from there."
Elliott has scored one goal in 18 games for Carlisle so far this season.