When they pulled over Reyes-Zavala's 2001 Nissan, police determined he was driving under the influence of an alcoholic beverage, according to a news release.
Police also said a girl, 6, was a passenger in the backseat and was not wearing a seat belt.
The child, who is not related to Reyes-Zavala, was released to her mother, police said. The mother is Reyes-Zavala's girlfriend, police said.
Reyes-Zavala was arrested on charges of aggravated driving while intoxicated, driving while intoxicated, aggravated unlicensed operation of a motor vehicle, endangering the welfare of a child and several traffic violations.
He is scheduled to be arraigned Tuesday at First District Court in Hempstead.
Under Leandra's Law, passed in November, 2009, drivers who are intoxicated or impaired by drugs with a child younger than 16 in the vehicle can be charged with a felony. The law was passed after the death of Leandra Rosado, 11, a minivan passenger who was killed in a DWI accident in Manhattan.