The car was stopped by West Yorkshire Police officers on Jack Lane in Hunslet.
The driver had a two-year-old child in the car and was arrested on Saturday night.
A tweet on the West Yorkshire Police Roads Policing Unit account said: "Jack Lane, Hunslet, Leeds - Driver stopped and was twice the legal drink drive limit.
"It’s never acceptable, but to make it worse, there was a two year old child in the car.
"Driver arrested. #DontDrinkAndDrive #Team4 #Fatal4 #SaferCommunitiesForAll #WYPTheCost"