The 34-year-old was treated on the pitch after a collision with Reds' defender Joel Matip, but opted to play on to the final whistle.
He had missed the 26 December defeat by Manchester City with the same injury.
"It could be the next three to four weeks," said manager Brendan Rodgers of Vardy's absence.
Fellow striker Patson Daka is out for another two-three weeks after limping out of the team's Carabao Cup defeat by Liverpool, while forward Kelechi Iheanacho has been called up to the Nigeria squad for the Africa Cup of Nations along with team-mate Wilfred Ndidi.
The tournament begins on 9 January, with the final on 6 February.
Vardy, who has scored 11 goals in 22 appearances this season, adds to a lengthy injury list at Leicester that features another seven players.