As long as the bark is not skinned all the way around, it will most likely heal itself and be OK. There seem to be mixed opinions about wrapping a wounded plant. A wound is a great place for insects to enter a plant. Some say that wrapping such a wound provides an even better environment for the insects to set up house keeping than if you just left it alone. I don't know.
I have an oak with a trunk about 12" now. When it was maybe 6", borers attacked it and almost destroyed it. I sprayed the borers and killed them. But a gap in the trunk about 3" wide from the ground up to about 5' and I don't know how deep just died. After seeing how much damage there was, I decided to cut it down. But I forgot about it for a while and when I decided to go ahead and cut it down, I noticed fresh growth around the edges of the dead area. I decided to let it go and after about 4 years you can barely tell it was ever damaged. I planted another tree of the same size at the same time as that one. The damaged tree is only slightly smaller than the other. Plants have a pretty amazing ability to recover.