 Kövess' father was a senior military officer living in Temesvár, Kingdom of Hungary, Austrian Empire (now Timișoara, Romania).His mother came from Fogaras (now Făgăraș, Romania), where her Thuringian father worked as a pharmacist; her mother was a Transylvanian Saxon from Hermannstadt (now Sibiu, Romania).He married the Baroness Eugenie Hye von Glunek in 1892 and they had 3 sons; Adalbert, who was killed in action in 1914 and Géza and Jenő who served as artillery officers.