The 27-year-old was unable to play for Holland over the last week because of the injury and has spent the last fortnight receiving treatment in Munich.
Only yesterday, Bayern's director of sport Christian Nerlinger had said the break had done Robben good and that he should be back to face Freiburg, but Heynckes has now revealed that is not the case.
"He will not be playing," said the Bayern coach. "It is not a very pleasant situation for him.
"He has got to be pain-free, and then he can play.
"I cannot say when he can play again, but it is not particularly a good sign that we cannot give a precise estimation."
Heynckes had hoped Robben would have taken part in full training in preparation for Saturday's clash with Freiburg, but now the Dutchman must also be regarded as a doubt for next Tuesday's Champions League match with Villarreal.
"We just have to take the situation as it is and we can compensate for his loss with a united team performance," added Heynckes.