The 25-year-old sustained the injury during his side’s 1-0 victory away at Aberdeen on Sunday.
The Honduran international fell awkwardly when contesting a ball with the Dons’ Peter Pawlett.
"It's a huge blow for us to lose him and we don't know how long he is going to be out for," Lennon told BBC Radio Scotland.
"He is being assessed at the minute and we'll know whether he requires surgery and, if he does, he will be out for three months anyway."
"We might have to look for another left-back," he added.
Celtic signed Izaguirre from Honduran side Montagua for £400,000 in 2010 and the defender won all four major players’ honours in his first season at Parkhead.