He was a first-begotten child in the family of Alexey Pavlovich Kravkov (1857–1895), the senior doctor of the 11th «Fanagoriyskiy» Grenadiers Regiment, and his wife Antonina Ivanovna.

After Alexey Kravkov's death his widow together with her younger son Leonid moved to Moscow, leaving Maximilian with relatives in Ryazan.

Early in 1908 Maximilian Kravkov together with students Bystrovzorov, Orlov and pharmaceutist Babkov created an autonomous fighting group with the aim to prepare an attempt upon the life of the Moscow Governor General Sergey Gershelman.

In 1909, the Moscow Military Region Court found Maximilian Kravkov guilty of “keeping explosives and bursting charges” and sentenced him to five years of solitary confinement.

After the amnesty in March 1917 he joined the Union of Socialists-Revolutionaries-Maximalists, was elected a member of the Tayshet Executive Committee and was sent to the Uyesd Congress to Nizhneudinsk.

After the restoration of the Soviet power in Siberia Maximilian Kravkov was in charge of the Museum of Local Lore, History and Economy in Irkutsk.

In 1920–1921, Maximilian Kravkov lived and worked in Omsk where he was appointed chief of Subdepartment of Museums in the Siberian Department of Public Education.

At the end of 1920th – beginning 1930th Kravkov as a member of geological exploratory and geographic expeditions used to visit the Sayan Mountains and the lower reaches of the Yenisei River.

The first significant results of Maximilian Kravkov's efforts to popularize knowledge of Siberia were his books “Chto takoe muzei I kak ego ustroit v derevne” (What is a museum and how to organize it in a village, 1921), “Yestestvennye bogatstva Sibiri” (Natural resources of Siberia, 1928), “Programma-instruktsiya po geologicheskim izucheniyam i sboram (Programm-instruction on geological researches and collections, 1929) and his article on geology and geography works in a volume “Abakanskaya ekspeditsiya.

In 1924 Maximilian Kravkov, who was also in charge of Sibkino, took an active part in the work at the “first Siberian movie” titled “The red gas” (1924), shot on Vladimir Zazubrin's writings.

His last books were the novel “Utro bolshogo dnia” (Morning of a great day, 1936) and a collection of stories “Zolotaya rossyp” (Placer gold, 1936).

Maximilian's younger brother Leonid Alexeyevich Kravkov (1889 – after 1930), captain of the 5th artillery brigade, participated in the World War I, on 10 May 1917 he was awarded with St. George Sword.