The crash was reported at 1:51 p.m. on Port Chicago Highway at Lynbrook Street and Riverside Drive in unincorporated Contra Costa County, CHP Officer Nicole Pacheco said.
CHP Officer Tom Maguire said the man told officers that he had been celebrating his birthday by getting drunk and racing another driver.
He appears to have crashed into another vehicle during the race and then he and his daughter fled the scene on foot.
He was arrested a short distance away on suspicion of driving under the influence of alcohol and child endangerment.
Neither the man nor his daughter appeared to be seriously injured, but an ambulance was called for the child. She was taken to Contra Costa Regional Medical Center in Martinez to be examined.
The case has been referred to Child Protective Services, Maguire said.
Information about the other vehicle involved in the crash was not immediately available.
