Fasting has some medical applications. Among them is pre-operative fasting which involves wounds.
But wound healing is basically a status of greatly increased nutritional demands. So, yes, fasting while wounded tends to be a not so good idea:
Basics in nutrition and wound healing:
Therefore, local wound management and good documentation of the wound is essential for non-delayed wound healing and prevention of the development of chronic wounds. During the wound-healing process much energy is needed. The energy for the building of new cells is usually released from body energy stores and protein reserves. This can be very challenging for undernourished and malnourished patients.
From that article:
Influence of undernutrition on wound healing
Even in uncomplicated starvation, as during a prolonged fasting, the body of an average adult subject loses 60 to 70 g of protein (240–280 g of muscle tissue) per day. However, severe trauma or sepsis can increase the loss of body protein up to 150 to 250 g (600–1000 g of muscle tissue) per day. Wound healing is delayed in subjects who had periods of starvation (simple or stress starvation) before injury or a surgical procedure due to the lack of endogenous substrates. Further undernutrition impedes wound healing in addition to:
- Delayed neovascularization and decreased collagen synthesis
- Prolonged phase of inflammation
- Decreased phagocytosis by leukocytes
- Dysfunction of B and T cells
- Decreased mechanical strength of the skin
Proteins
Proteins play the most important role throughout the entire wound-healing process. Lymphocytes, leukocytes, phagocytes, monocytes, and macrophagesdimmune system cellsdare mainly comprised of proteins and are necessary to initiate a healthy inflammatory response in the healing process. An adequate supply with proteins is necessary for consistent wound healing. Because collagen is the protein that is produced mainly in the healing wound, a lack of protein decreases the synthesis of collagen and the production of fibroblasts.
Of course, all proteinogenic amino acids are important during wound healing. There is evidence that some amino acids are especially important for the process. Methionine and cysteine are involved in the synthesis of connective tissue and collagen. Arginine is thought to have a major influence on the proliferation of collagen accretion and on an improved immune reaction.
And of course there is an increased need for fatty acids, vitamin C, iron, zinc etc. From a surgeon's perspective these points need to be considered:
The metabolic effects of fasting and surgery:
- fasting rapidly affects metabolism, although gradually adaptation occurs to minimize protein losses
- surgery increases metabolic rate and catabolism, of which insulin resistance is related to the magnitude of surgery
- insulin treatment in insulin-resistant patients after surgery or trauma markedly improves body metabolism and reduces morbidity and mortality
- avoiding preoperative fasting reduces postoperative insulin resistance by about 50% and attenuates postoperative impairment in nitrogen losses, lean body mass and muscle function
- fasting or deficient energy intake after surgery does not affect postoperative insulin resistance but does accelerate nitrogen losses
- perioperative parenteral nutrition has been shown to reduce morbidity and mortality in patients with malnutrition, but has no beneficial effects in well fed patients
- oral supplements perioperatively may attenuate postoperative weight loss and reduce infectious complications
- patients undergoing surgery within a multimodal programme designed to reduce stress and to improve postoperative function display only minor insulin resistance, which allows feeding without hyperglycaemia

For a more comprehensive view of nutrition and wound healing, take a look at
Nutrition, Anabolism, and the Wound Healing Process: An Overview:
One is activation of the stress response to injury, and the second is the development of any protein-energy malnutrition (PEM). Any significant wound leads to a hypermetabolic and catabolic state, and nutritional needs are significantly increased. The healing wound depends on adequate nutrient flow. Of particular concern is the presence of any PEM, PEM being defined as a deficiency of energy and protein intake to meet bodily demands. PEM in the presence of a wound leads to the loss of lean body mass (LBM) or protein stores, which will in and of itself impede the healing process. Early aggressive nutrient and micronutritional feeding is essential to control and prevent this process from developing. PEM is commonly seen in the chronic wound population, especially the elderly, disabled, or chronically ill populations where chronic wounds tend to develop.