Sturridge ruled out for six to eight weeks
Sturridge, who had suffered with a thigh injury sustained ahead of September's Premier League win over Manchester United, had looked set to return for Sunday's clash with Hull City.
However, Rodgers revealed ahead of that game that Sturridge injured his ankle in training on Friday and could miss up to two months as a result.
Rodgers had previously voiced his displeasure at Sturridge playing the full 90 minutes for England in their 1-0 friendly defeat against Germany last month, describing him as being "not right" in training prior to last Saturday's Merseyside derby.
However, the 24-year-old made a substitute appearance for Liverpool in their 3-3 draw with Everton at Goodison Park, scoring a late equaliser.
"Daniel is probably going to be out six-to-eight weeks," Rodgers told Sky Sports. "It was something we thought was never going to be as serious as that to be honest.
"He slipped over in training and we thought initially it was his toe. He got brought inside straight away and he was taken for a scan straight away and it showed he'd actually got a ligament strain.
"It's a big blow for us because he's been brilliant since he's come in.
"We've played a few systems this year, which has been brilliant, and it's given me the flexibility to change it around. It's about the players and we've got some good ones to come in."
Sturridge is the highest-scoring Englishman in the Premier League, with nine strikes to his name, and only Manchester City's Sergio Aguero has more with 10.
The injury leaves Rodgers with just one fully fit striker in the shape of Luis Suarez - who has also scored nine league goals this term - although Iago Aspas returned to the bench for Sunday's clash at the KC Stadium after a thigh problem.