A motorist apparently called 911 to report a vehicle traveling erratically.
Police say 24-year-old Paul Amay had a blood-alcohol level measuring .29. That's more than three times the legal limit.
Officers say they also found the baby unrestrained in the back seat of the car.
Amay was charged with drunken driving and endangering the welfare of a child, which are both misdemeanors.
Amay's DWI charge could be upgraded to a felony based on the Westchester County District Attorney Office's review of the case.
Last week, Gov. David Paterson signed the Child Passenger Protection Act, now known as Leandra's Law, which makes it a felony for individuals to drive while intoxicated or under the influence of drugs with children under age 15 in the car.
However, that law will not go into effect until 30 days after Gov. Paterson signed it.