Jenny Rivera, 52, a professor at the City University of New York School of Law, would replace Carmen Ciparick, who stepped down from the Court of Appeals after reaching the mandatory retirement age of 70.
Ciparick's departure left the seven-member court without a Hispanic judge -- until Rivera's nomination.
The nomination for a 14-year term requires State Senate confirmation.
Elena Goldberg Velazquez, president of the Puerto Rican Bar Association, said Cuomo was "nominating an extraordinarily qualified Latina to New York's highest court."
Rivera has been an associate counsel at the Puerto Rican Legal Defense and Education Fund. She also worked under Cuomo when he was state attorney general and she was a clerk to U.S. Supreme Court Justice Sonia Sotomayor when the latter served on a federal district court.