Ivan Georgievich Petrovsky, also Petrovskii (Russian: Ива́н Гео́ргиевич Петро́вский) (18 January 1901, Sevsk – 15 January 1973, Moscow) was a Soviet mathematician in the field of partial differential equations, and studied Petrovsky lacunas. He greatly contributed to solution of Hilbert's 19th and 16th problems. He also worked on the boundary value problem, probability, and topology of algebraic curves and surfaces.

Petrovsky was a student of Dmitri Egorov. Among his students were Olga Ladyzhenskaya, Yevgeniy Landis, Olga Oleinik and Sergei Godunov.

Petrovsky taught at Steklov Institute of Mathematics. He was a member of the Soviet Academy of Sciences since 1946 and was awarded Hero of Socialist Labor in 1969. He was the president of Moscow State University (1951 - 1973) and the head of the International Congress of Mathematicians (Moscow, 1966). He is buried in the cemetery of the Novodevichy Convent in Moscow.