The 34-year-old picked up the injury in the Carabao Cup defeat to Liverpool last week but soldiered on to complete the game.
Vardy was rested for the 6-3 defeat to Manchester City over the weekend but aggravated the injury on his return in the 1-0 win over Liverpool on Tuesday in the Premier League.
Foxes manager Brendan Rodgers has revealed that the former England international will be missing in action for up to four weeks and has attributed the injury to the high number of games played within a short period of time.
"Jamie will be out," said Leicester manager Brendan Rodgers. "It could be the next three to four weeks.
"It's a hamstring. He could soldier on, which is what he wanted to do, but the scan has shown up as that."
"I think the fatigue element in that combination of games has probably led to it," added Rodgers.
"The players are not robots. People think, because they are paid a lot of money, they should turn out and play every single day of the week and that's not the case.
"He felt it in the cup game at Liverpool, where the last half-hour it was hindering his performance.
"We didn't involve him at the weekend to give him maximum rest - even though he was on the bench he wasn't able to play - and the other night he just felt it towards the end of the game.
"It's the combination of games we have had and the recovery time has made it difficult for him."
Vardy has scored 11 goals in 22 appearances across all competitions this season.
