Background Providing quality care is of the fundamental elements of holistic nursing practice, and burnout and moral intelligence of nurses be mentioned as the important factors influencing the quality of nursing care. The present study was conducted to investigate the relationship between moral intelligence, burnout, and the quality of nursing care. Methods This descriptive-correlative study was conducted on 125 nurses working in Sari-based Educational hospitals affiliated to Mazandaran University of Medical Sciences, Iran, between June and August 2020. The sample was selected via random sampling. The data were collected by the Maslach Burnout Inventory, Lennick and Kiel Moral Intelligence Scale, and Quality of Patient Care Scale. The data were analyzed by SPSS-21 and Amos-24. Results A direct and significant relationship was found between the quality of nursing care and moral intelligence ( r = 0.285, p = 0.001). Quality of care had an inverse relationship with subscales of frequency of burnout including emotional exhaustion ( r = −0.369, p < 0.001) and depersonalization ( r = −0.471, p < 0.001) and also, a direct relationship with personal accomplishment ( r = 0.226, p = 0.011). The findings also showed an inverse relationship between quality of care and subscales of the intensity of burnout. Amos software yielded results that demonstrated moral intelligence as a robust mediator between burnout and the quality of care. Conclusion The findings implied the necessity for more attention to moral intelligence as a mediator in order to come up with properly managing the personality traits influencing the nurses’ burnout reduction, which can ultimately lead to improved quality of nursing care.