Sixteen 35-day-old male crossbred rabbits (New Zealand white × Thai native breed) with an initial weight of 484 ± 11.3 g were randomly divided into two groups of eight, constituting control and treatment groups. The treatment group was orally administered a crude extract of butterfly pea (Clitoria ternatea L.) at 0.5 g/kg body weight from weaning (at 35 days) to slaughter (at 90 days). The effects on the phagocytic activity of blood polymorphonuclear leukocytes, serum biochemistry, meat quality, muscular lipid peroxidation, the apparent digestibility of dry matter and nutrients, and gut histology were studied. The results revealed that the phagocytic function of circulating leukocytes (75 and 90 days) and alveolar macrophages (90 days) did not differ between the two groups. At slaughter, treated rabbits had lower blood urea nitrogen concentrations and higher liver weight than control rabbits (p < 0.05). After chilling at 4 °C for 24 h, a lower meat pH and the alteration of meat color (brighter, less yellow, lower hue angle, and decreased color saturation) were observed in the treated group (p < 0.05). Furthermore, lipid peroxidation (measured at 3, 5, and 7 storage days) in the meat of treated rabbits was lower than in controls (p < 0.05). The apparent digestibility of organic matter and ether extract (analyzed at 46 days for 4 days) was improved in the treated group (p < 0.05), whereas gut histology was unaffected. In conclusion, butterfly pea extract supplementation did not affect phagocytic function but led to a modification in meat color, delayed lipid peroxidation, and improved digestibility.