Mashkevich was born in Frunze, Kyrgyz SSR, Soviet Union, in 1954. His Father Anton, a Doctor born in Lithuania, and his mother, Rakhel Yoffe, a Lawyer born in Vitebsk, were evacuated to Kyrgyzstan in 1941. His family background is Lithuanian Jewish. He is a graduate of Kyrgyz State University where he studied philology. Mashkevich started out an academic career but became a businessman during perestroika. Mashkevich, Patokh Chodiev, and Alijan Ibragimov form "the Trio," a group of Kazakh businessmen who became billionaires. The Trio gained control of the recently privatized chromium, alumina, and gas operations in Kazakhstan (some of the largest ones in the world).