Kirill Maximov was born in Chișinău, the capital city of the Republic of Moldova. At the age of five, he received his first violin lessons from Alla Guseva at the Sergei Rachmaninov Special Music School. From 2002 to 2003, he studied in Bordeaux with Robert Papavrami, and in 2017 he graduated with honors from the University of Music and Performing Arts in Vienna under the tutelage of Dora Schwarzberg. He has attended masterclasses with Koichiro Harada, Marianne Piketty, Taras Gabora, Lothar Strauß, Igor Ozim, Hubert Kroisamer, and Krzysztof Węgrzyn.

Kirill Maximov is the prize winner of many international violin competitions, including the Mykola Lysenko Music Competition in Kiev, the Villa de Llanes Violin Competition in Spain, the Competition Young Virtuosos in Sofia, Bulgaria, the Stefanie Hohl Violin Competition, and the Fritz Kreisler Violin Competition in Vienna. From 2017 to 2024, he was the first concertmaster of the Tonkünstler Orchestra. Since April 2024, Kirill Maximov has been the first concertmaster of the Vienna Symphony Orchestra. Furthermore, he has performed as a guest concertmaster during a two-week Japan tour in 2020 with the Hyogo Performing Arts Center Orchestra (PAC), conducted by Tonkünstler Chief Conductor Yutaka Sado. Kirill Maximov has performed as a soloist with numerous orchestras, including the Southwest German Chamber Orchestra Pforzheim, the Moldavian National Symphony Orchestra, the Kiev Symphony Orchestra, and the Oradea Philharmonic Symphony Orchestra. Highlights of his career include solo performances in the Great Hall of the Vienna Musikverein under the direction of Yutaka Sado, Fabien Gabel, and Jun Märkl. As a chamber musician, he has worked with Rudolf Buchbinder, Dora Schwarzberg, Jörg Widmann, Emmanuel Tjeknavorian, Alena Baeva, and Dieter Flury.

Kirill Maximov plays the "Antonio Stradivari ex Baron Oppenheim" violin built in Cremona in 1716, on loan from the collection of the Austrian National Bank, as well as a violin made in 2021 in the workshop of the multiple award-winning violin maker Stephan von Baehr in Paris.