Zakharova was born in Lutsk, Ukrainian SSR, Soviet Union, on June 10, 1979. At age six, Svetlana was taken by her mother to learn folk dancing at a local studio. At age 10, she auditioned for and was accepted into the Kiev Choreographic School. Just four months later, however, her father's reassignment in the army to East Germany forced Svetlana's withdrawal from school. Six months later, her family returned to Ukraine and Svetlana auditioned again for the Kiev Choreographic School. She was readmitted and immediately joined the second class, under teacher Valeria Sulegina.
In 1996–1997, she debuted with the Mariinsky Ballet, appearing as Maria with Ruben Bobovnikov, in Rostislav Zakharov's The Fountain of Bakhchisarai. In 2003–2004, she accepted a long-standing open offer with the Bolshoi, reportedly due to discontent with the Mariinsky.
Today, Zakharova tours and guests with the world's great ballet companies. She is considered one of the greatest ballerinas of the generation and is highly regarded for her technical expertise, her exquisite footwork and her exceptionally high extensions, as well as her musicality. Not all critics find her extreme positions aesthetically pleasing as they do not conform to 'classical' norms.
She is married to Russian violinist Vadim Repin. The couple have one child, a daughter Anna, who was born on February 17, 2011. Zakharova had withdrawn from the Bolshoi Ballet tour to London in the summer of 2010 citing a hip injury; in fact she was pregnant at the time. Zakharova returned to dancing, and performed in London on May 15, 2011, in a gala performance celebrating Soviet ballerina Galina Ulanova.