Aleksandr Sholokhov was born on 25 January 1962 in Moscow. He is a grandson of novelist Mikhail Sholokhov. Aleksandr Sholokhov graduated from the Biology and Soil Faculty of Rostov State University in 1984 and later worked as a lecturer there. He also studied at the graduate school of Moscow State University.
Since 1989 he was an employee of the National Sholokhov Museum-Reserve. In 1999 he graduated from Rostov State Economic University, majoring in law. In 2001–2016 he was the Director of National Sholokhov Museum-Reserve. In 2003–2008 he was a deputy of the Legislative Assembly of Rostov Oblast. In 2014 he became a member the Presidium of the Council under the President of the Russian Federation for Culture and Art. In 2016—2022, he was the President of the Russian Committee of the International Union of Museums. On 18 September 2016 he was elected a deputy of the 7th State Duma. He is a deputy chairman of the State Duma Committee on Culture.