Sturridge, who has already missed five months of the season through injury, was sent home from international duty earlier this week ahead of Friday's Euro 2016 qualifier against Lithuania and a friendly against Italy on Tuesday.
The striker, who suffered the injury in Liverpool's 2-1 Premier League defeat by Manchester United on Sunday, could now be out for around a month, according to British media reports.
With Liverpool having slipped five points behind fourth-place United in the battle for Champions League qualification, the injury will be a major headache for the Merseysiders heading into the season's climax.
"I'm disappointed for Daniel because he didn’t really feel that it was any problem," Hodgson told reporters.
"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.”
Should Sturridge be ruled out for four weeks, he would miss Liverpool's Premier League games against Arsenal and Newcastle United, their FA Cup quarter final replay against Blackburn Rovers and a potential semi-final against Aston Villa.
(Reporting by Toby Davis; editing by Patrick Johnston)
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