Sturridge has already been out of action for six weeks due to a thigh strain he picked up on international duty.
The 25-year-old had hoped to make his comeback on Sunday when Liverpool travel to Queens Park Rangers in the Premier League.
But, according to the Liverpool Echo, the former Chelsea forward pulled his calf during training on Thursday and could now be absent for up to another month.
He has already been sorely missed by Liverpool, who have struggled to emulate last season’s free-scoring form, and is likely to be out of action for the Reds’ Champions League double-header against Real Madrid and England’s Euro 2016 qualifying match against Slovenia.
“Daniel has pulled his calf,” Rodgers told the newspaper. “He’s looking at being out for another two to four weeks.
“It’s a big blow as we were looking forward to welcoming Daniel back. He has worked tirelessly.
“But we have other players training hard and working hard and we will turn to them. It’s why we bulked up the squad in the summer.”