Grainger suffered a partial tear of his anterior cruciate ligament in Saturday's 0-0 draw at Motherwell and is awaiting news from a consultant before the full prognosis is known.
Speaking ahead of Wednesday's SPL clash with Celtic at Tynecastle, manager John McGlynn said: "Danny Grainger has a partial tear of his ACL. We are still waiting on the consultant to give us a bit more information, whether he will need surgery or not.
"We're hoping he's not going to need surgery. I'm gutted for Danny that he's going to miss a good part of the season. It's a shame. He's a good lad and he's been a good professional for Heart of Midlothian Football Club.
"He's one of our top goalscorers this season with three goals from left-back, which is an excellent return."
Kevin McHattie could deputise for Grainger against SPL champions Celtic, or Ryan McGowan could switch flanks from right-back.