Daniil Medvedev was born in Moscow to Sergey Medvedev and Olga Medvedeva on 11 February 1996. He has two older sisters,Julia and Elena, respectively 12 and 8 years older. When he was 6 years old, his mother noticed an advertisement for group tennis lessons at the pool where he was taking swimming lessons. His father, an engineer, encouraged him to join. Medvedev's first tennis teacher was Ekaterina Kryuchkova, a former coach of, among others, professional tennis player Vera Zvonareva. With his family, he moved to Antibes, France, where she trained at the tennis academy. His parents have lived in France ever since, as pensioners.
Medvedev studied physics and mathematics at a specialized school, before graduating early and enrolling in business and economics at the Moscow State Institute of International Relations. He later dropped out to focus on tennis. Later he moved to the Russian State University of Physical Education, Sports, Youth and Tourism, where he obtained a coaching diploma. Medvedev was listed as ineligible for mandatory military service in the Russian Armed Forces due to his minor health problems due to his 8-month preterm birth. Like many other Russian tennis players, Medvedev considered switching to the flag of Kazakhstan early in his professional career due to lack of support from the Russian Tennis Federation. Sports psychologist Francisca Dauzet is part of his French-speaking entourage.