This is not the first symptom of diabetes, but it is often the wake-up call that persuades people to go to the doctor. High blood glucose levels would impair many different functions in the body, including the normal healing rate.
First off, diabetes causes an alteration to the micro-circulation. High blood glucose impairs the normal blood flow to the tissues, and this would make it more difficult to coagulate and repair any lesion to the skin or underlying tissues. Additionally, it slows down the body response against infection, which further slows down the healing process.