The 21-year-old has missed 18 matches in all competitions for the Hoops this term, and Lennon, who has been playing Emilio Izaguirre at left-back in Tierney’s absence, admitted the Scotland international is in “too much discomfort to play”.
He added: “He is seeing a specialist on Thursday. We will have to go with what we are advised by the specialist.
“He has played for quite a while but it has got to the point where he is in too much pain.”
Celtic have matches remaining against Kilmarnock and Hearts at home, with trips to Aberdeen and Rangers in between.
Today’s goalless draw with Hibs extended their lead at the top of the Ladbrokes Premiership table to nine points.