(1) Background: The neem tree, Azadirachta indica (A. Juss), is a well-known species used in traditional medicine for the treatment of skin conditions such as irritation, eczema, burns, and wounds. The objective of the current study was to investigate the physicochemical and wound-healing properties of A. indica fruits. (2) Methods: Gas chromatography coupled with mass spectrometry (GC-MS) was used to determine the content of fatty acids and phytosterols, and high-performance liquid chromatography (HPLC) was used to determine the tocopherol content. The wound-healing activity was observed on the backs of six adult male rabbits. (3) Results: The results showed that the plant contained fatty acids, as well as oleic (46.05%), palmitic (23.94%), linoleic (11.39%), and stearic (7.87%) acids. The phytosterols were three major compounds; in decreasing order of importance, they were β-sitosterol (97.26 mg/100 g), campesterol (18.94 mg/100 g), and stigmasterol (12.05 mg/100 g). There were also traces of cholesterol. The neem was a moderate source of vitamin E (α-tocopherol, 14.86 mg/100 g). The hexane extracts showed no acute toxicity and low eye and skin irritability and had reasonable safety and important wound-healing activity. (4) Conclusions: The results confirmed that A. indica is a valuable source of fatty acids, phytosterols, and vitamin E and is efficient in the process of wound healing.