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).

ENRC was floated on the London Stock Exchange in December 2007, with a market capitalisation on Admission of approximately £6.8 billion.

With his partners Chodiev and Ibragimov, Mashkevich helped to develop these assets, and is a major shareholder in Eurasian National Resources Corporation (ENRC), now one of the world's leading natural resources groups. ENRC, based in London, operates a number of metals assets in Kazakhstan and Africa, having acquired numerous mining operations in Eastern Europe and Africa. In 2009, ENRC generated a $1,462 million profit on sales of $3.8 billion.

As of 2010 he is on the Forbes list of billionaires at #287. As of 2017 he is on the Forbes list of billionaires at # 1098 with a worth of 1.9 Billion.

On April 6, 2011, Mashkevitch announced his intention to found a Jewish version of Al-Jazeera that will "represent Israel on an international level, with real information."