Mihály was born on February 28th, 1748. Mihály's father was István Magyary-Kossa and his mother was Zsuzsanna Borbély. His paternal grandparents were Péter Magyary-Kossa and Judit Sándor. He had a brother named István. He was the older of the two children. He died at the age of 32 on June 25th, 1780.