The former England international, 35 next month, had complained of an issue in the Carabao Cup defeat at Anfield last week, was rested for the Boxing Day trip to Manchester City but played and then sustained the injury in Tuesday’s win at home to Liverpool.
Playmaker James Maddison is fit after he came off against Jurgen Klopp’s side but with Patson Daka also injured, forcing him to miss the Africa Cup of Nations, it leaves manager Brendan Rodgers with just Kelechi Iheanacho – himself joining up with Nigeria next week – and Ayoze Perez as options up front.
That is in addition to at least seven other players still currently sidelined.
“Jamie will be out. It could be the next three to four weeks,” said Rodgers.
“It’s a hamstring. He could soldier on, which is what he wanted to do, but the scan has shown up as that.”
Rodgers felt the packed festive schedule and the extra demands placed on players due to Covid had played a significant part in Vardy’s injury.
“I think the fatigue element in that combination of games has probably led to it,” he added.
“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.”
Daka was already out, having limped off at Anfield with a hamstring problem, but the extent of the issue means the Zambia international will not be joining up with his country after this weekend’s Premier League matches.
“Patson will not be going. He’s not fit. He will stay and hopefully within the next two to three weeks will be back again,” said Rodgers.