The eldest son of Ivan Popov (ca. 1732–1783) and his wife Tatyana (ca. 1736–?), Mikhail studied at the Kiev Academy (1763–1769) and the Aleksandr Nevsky Seminary in Saint Petersburg (1770–1774). He was appointed Deacon at the Nikolayevsky Cathedral in Saint Petersburg in 1774, and at the Church of Saint Sergiev from 1790.
On 1/12 June 1774 he married Anna Dmitriyevna Rykovskaya (ca. 1752–ca. 1823) at the Church of Saint Sergiev in Saint Petersburg, and they had five children: Varvara (b. 1776); Yekaterina (1778–1816), grandmother of the composer; Nikolay (1779–1869); Maria (b. 1783); and Sergey (1785–1851).
Mikhail Popov died from a fever on 16/27 March 1792 in Saint Petersburg, and was buried at the city's Otkhensky Cemetery.