Why do healing wounds itch?

Histamine release. Whenever tissue is subject to trauma, the body initiates an inflammatory response as part of the healing process. Several different types of cells are released into the bloodstream and make their way to the wound where healing is initiated. Among these are mast cells which release histamine. It is the histamine which causes the wound to itch.
Normal process. Blood cells such (white blood cells, platelets) and other tissue cells release chemical factors called cytokines that initiate healing. This results in a response with some features in common with an allergic reaction. Itching is a normal part of this response and is actually a good sign that the wound is healing properly.
Itching in the wound. Complicated but scientists believe that the itching is due to histamine in the healing tissue which causes the itching.