Afanasy Bagration was married to Ana Amilakhvari (Anna Vasilyevna; 10 April 1720 – 6 March 1794), also a Georgian expatriate noblewoman, a daughter of Prince Vakhtang (Vasily) Amilakhvari (died 1739) by his wife, Princess Elene Orbeliani (). Afanasy and Ana had three children—Anton, Varvara, and Ana.
