Grandview police say the chase early Sunday sometimes reached 100 mph before officers stopped following the car.
Eventually, the car was abandoned and police found the 2-year-old boy in the back seat, not in his car seat.
Kansas City and Grandview police searched the area where the car was abandoned and found the man hiding in a creek in waist-deep water.
The man was taken to a hospital for hypothermia.
Police say he appeared to be under the influence of drugs. He faces possible charges of child endangerment. The boy was placed in state custody.