The striker has not played since August after injuring his hamstring while on England duty, but had been expected to feature in Brendan Rodgers's squad for their match against Queens Park Rangers this weekend.
However, the manager told the Liverpool Echo: "Daniel has pulled his calf. 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 an working hard and we will turn to them. It's why we bulked up the squad in the summer."
Sturridge scored 21 goals for Liverpool last season.