Mikhail Muraviev was the son of General Count Nicholas Muravyov (governor of Grodno), and grandson of the Count Mikhail Nikolayevich Muravyov-Vilensky, who became notorious for his drastic measures in stamping out the Polish insurrection of 1863 in the Lithuanian provinces. He was educated at a secondary school at Poltava, and was for a short time at Heidelberg University.
In 1864, he entered the chancellery of the minister of foreign affairs at St.Petersburg, and was soon afterwards attached to the Russian legation at Stuttgart, where he attracted the notice of Queen Olga of Württemberg. He was transferred to Berlin, then to Stockholm, and back again to Berlin. In 1877, he was second secretary at the Hague. During the Russo-Turkish War of 1877-78, he was a delegate of the Red Cross Society in charge of an ambulance train provided by Queen Olga of Württemberg.
After the war, he was successively first secretary in Paris, chancellor of the embassy in Berlin, and then minister in Copenhagen. In Denmark, he was brought much into contact with the imperial family, and, on the death of Prince Lobanov-Rostovsky in 1897, he was appointed by the Tsar Nicholas II to be his minister of foreign affairs.
The next three and a half years were a critical time for European diplomacy. The Chinese and Cretan questions were disturbing factors. As regards Crete, Count Muraviev's policy was vacillating; in China, his hands were forced by Germany's action at Kiaochow. But he acted with singular regret with regard at all events to his assurances to Britain respecting the leases of Port Arthur and Talienwan from China; he told the British ambassador that these would be open ports, and afterwards essentially modified this pledge.
When the Tsar Nicholas inaugurated the Peace Conference at the Hague, Count Muraviev extricated his country from a situation of some embarrassment; but when, subsequently, Russian agents in Manchuria and Peking connived at the agitation which culminated in the Boxer Rebellion of 1900, the relations of the responsible foreign minister with the tsar became strained. Muraviev died suddenly on June 21, 1900 of apoplexy, brought on, it was said, by a stormy interview with the tsar.