Schwarzer and Fulham had been enjoying a good run of defensive form before the Swansea defeat, with only Manchester City (15), Manchester United (14) and Liverpool (13) conceding fewer goals then Fulham (18) this season.
The Australian custodian sustained the spinal injury in Fulham's 2-0 defeat at Swansea on Saturday, after falling awkwardly when catching a cross.
Schwarzer took to Twitter to thank fans for their concern and to express his disappointment at the injury:
"Thanks for your well wishes, I'm devastated to be out for 4-6 weeks," he wrote. "After speaking to the specialist, it was very clear I needed a rest."
Stockdale’s return will present him with a chance to claim a starting berth in Martin Jol's side in the 39-year-old's absence, with Schwarzer sidelined until January.
Since his move from Darlington in 2008, Stockdale has failed to gain a regular place in the side and has endured spells on-loan at Rotherham, Leicester, Plymouth Argyle and most recently Ipswich.
Despite mainly featuring in the Championship along with sporadic appearances for Fulham, Fabio Capello has given the 26-year-old numerous England call-ups but he is still yet to earn his first international cap.