Griffiths was forced off just minutes after scoring the winner in the first half of the Scottish Premiership clash with Hibs at Celtic Park.
The Scotland striker will now miss the Europa League clash against Zenit St Petersburg next month.
Manager Brendan Rodgers said: “Leigh is disappointed after having a series of knocks over the course of the season.
“You are probably looking up to four weeks [out] with his calf strain.”
Griffiths will be joined on the sidelines by Celtic goalkeeper Craig Gordon, who sustained a knee injury in the same match and has been ruled out for up to 12 weeks.
Rdogers added: “It’s sad news for Craig and for us but of course we will need to have that cover for someone to come in and support Dorus de Vries so that is something that we are looking at.
“Craig is a great professional and while we are saying 12 weeks we are hoping he will be back sooner than that.
“Dorus has been a very loyal number two has been very good in recent performances. He is calm and assured and experienced.”