The daughter of a wealthy artillery general, Kovalevsky was born in Moscow and brought up in the traditional manner on a large country estate, being educated only by an English governess. Her introduction to mathematics was unusual. One of the children's rooms of the family's large country house had temporarily been papered with Ostragradsky's lecture notes on calculus. Kovalevsky studied the notes as a child, and this gave her a grounding in the subject.

In 1867 the family moved to St. Petersburg and Kovalevsky managed to receive some more formal teaching at the Naval Academy. But the only socially acceptable way to continue her education was as a married woman. Consequently, in 1868 she entered into a marriage of convenience with Vladimir Kovalevsky, a young paleontologist and a translator of Darwin. They moved to Heidelberg in 1869 and two years later to Berlin. Although she could not be admitted to public lectures, Kovalevsky received private classes from Karl Weierstrass, who was so impressed with her work that he persuaded the Göttingen authorities to award her a doctorate in 1874 for a thesis on partial differential equations.

Despite this she remained unemployable as a female professional mathematician. In 1878 the Kovalevskys returned to Russia and speculated unwisely in property. Depressed by mounting debts, Vladimir committed suicide in 1883. By this time Weierstrass had arranged for Kovalevsky to be appointed to a lectureship in mathematics at the University of Stockholm. She died from pneumonia in 1891.

Kovalevsky is best known for her work in partial differential equations in which she extended some earlier results of Cauchy. She also won the Borodin prize of the French Académie des Sciences in 1888 for her memoir On the Rotation of a Solid Body about a Fixed Point.