In Thor we see him get killed near the end of the movie by the Destroyer that was sent by Loki.
Yet once he regains the hammer, all his injuries are gone.
The entire fight sequence is here.
- 0:53 his face is badly injured
- Starting at 1:00 we see Jane, Lady Sif, Loki, and the Destroy all seem to believe he is dead
- 1:42 Odin releases the tear
- 2:21 as the hammer flies his arm rises to grasp it
- 2:52 his face is uninjured
So the Mjolnir we've seen in the cinematic universe hasn't demonstrated any healing abilities. However in an alternate story it seems that it does (at at least the transformation it enabled):
Unfortunately for her, all progress from chemotherapy became lost whenever she used Mjolnir to transform into Thor. Since the magical transformation purged all toxins from Jane's body, it did so to the chemotherapy drugs, but left the cancer behind since it was part of her body.
Now in the scene he did "transform" into Thor, however, Loki and the Destroy's behaviors seem to be strong indicators that Thor actually was dead. I also have a hard time to believe that Odin's tear can bring someone back from so far away.
We know that Thor can be injured while using the hammer due to the events in Age of Ultron and Thor 2.