Sturridge, who pulled out of the England squad ahead of Friday’s Euro qualifier against Lithuania, suffered the injury against Manchester United last Sunday.
If the injury is confirmed by his club, Sturridge, who has already missed a large part of the season because of injury, is likely to sit out much of April.
That would see him miss Liverpool’s trip to the Emirates on April 4 to face Arsenal, their FA Cup quarter final replay against Blackburn and a potential semi-final against Aston Villa at Wembley.
Hodgson said: “I’m disappointed for Daniel because he didn’t really feel that it was any problem.
“When he did the scan he was devastated as he didn’t want to leave. He has a slight tear and you can’t play through that.”
Meanwhile, football expert Tony Gayle believes Sturridge must make sure that he returns to action when he is 100 per cent fit.
“It’s a shame for the boy actually because he’s chasing it,” he said. “You get one injury, you come back and you get compensatory injuries of that injury you had in the first place and you kind of chase it and chase the form you were in as well.
“Sharpness in a striker is such an important thing – that half a second thinking time – or that ability to press the button and accelerate away.
“Since he’s come back from the injury, he’s lost just that little bit of sharpness – still a very good player and he’ll be back again – but take your time, make sure you’re right and come back when you’re spot on I think.”