Cuomo said he will appoint a commission to select a location and an artist to create the sculpture.
"Justice Ruth Bader Ginsburg selflessly pursued truth and justice in a world of division, giving voice to the voiceless and uplifting those who were pushed aside by forces of hate and indifference," he said.
"As a lawyer, jurist and professor, she redefined gender equity and civil rights and ensured America lived up to her founding ideals -- she was a monumental figure of equality, and we can all agree that she deserves a monument in her honor."
Cuomo said the commission with reach out to the arts community, including art institutions and organizations, in its process to select a design and location for the statue.
Ginsburg died Friday after a battle with pancreatic cancer. She was 87.
She was born in Brooklyn in 1933 and attended James Madison High School in the borough.
New York City Mayor Bill de Blasio described Ginsburg as "an unparalleled hometown hero." He said the city will begin plans for a memorial and he ordered that all flags -- currently at half staff in memory of COVID-19 victims -- continue to be flown at half staff in Ginsburg's memory.
"Like so many of you, I'm crushed that we lost an incomparable icon," de Blasio said Friday night. "A daughter of Brooklyn. A tenacious spirit who moved this country forward in fairness, equality and morality. She was Ruth Bader Ginsburg. She never backed down from a fight. Tonight her hometown and world mourn."