The experienced vice-captain suffered the injury during Sri Lanka's tour match in Adelaide and is doubtful for the Test starting on Nov. 8 in Brisbane.
"I would say it's definitely a grade one tear but we will have to see when the MRIs are assessed," Sangakkara said.
Sri Lanka play Queensland in a three-day tour match starting on Friday. Prasanna Jayawardene is likely to replace Sangakkara as wicketkeeper.