The alleged attack occurred Sept. 10 in Gouverneur village, about 100 miles north of Syracuse, officials said.
The white girls face criminal charges of harassment and assault in juvenile court, The New York Times reported. A 28-year-old bus monitor, who is also white, was charged with endangering the welfare of a child for not intervening.
"I am appalled by the reports of the horrendous, 20-minute racist assault on a 10-year-old African American girl in the town of Gouverneur," Cuomo said in a statement Wednesday.
"That this was allegedly perpetrated by her own classmates, on a school bus with an adult monitor present, makes this incident even more shocking and troubling. When we put our children on the bus to school, we are entrusting others with our most precious resource and this was an egregious and inexcusable violation of that trust."
The small Gouverneur Central School District has about 1,500 students, of whom about 97 percent are white, according to the latest figures compiled by the state Department of Education. The district's African American enrollment is about half a percent, according to the 2018 data.
Gouverneur police and school officials could not be immediately reached for comment Thursday.
Cuomo said he has directed the New York State Division of Human Rights to investigate.
"In New York, violence of any kind towards others based on their race or religion is not only offensive and repugnant to our values, it is illegal," the governor added. "We will never allow hate to win — we will defeat it and we will continue to use every tool at our disposal to help ensure all our children are safe from hate."