Judging by the quote below, we see that Hermione shot some spell at Greyback that knocked him over and caused a great deal of pain on its own …
‘NO!’ shrieked Hermione, and with a deafening blast from her wand Fenrir Greyback was thrown backwards from the feebly stirring body of Lavender Brown. He hit the marble banisters and struggled to return to his feet. Then, with a bright white flash and a crack, a crystal ball fell on the top of his head and he crumpled to the ground and did not move.
- Harry Potter and the Deathly Hallows, Chapter 32
However, that last line is a bit vague. Did the crystal ball cause the white flash and crack, or did Hermione cast another spell on purpose that caused the ball to drop? So in essence Hermione would have killed Greyback on purpose, if in fact he is dead.
So two intertwined questions really … Is Fenrir Greyback dead, and did Hermione kill him?