Lt. Chris Sherry said the woman has been treated and released from a local hospital for the injuries she sustained in the collision at about 4:30 a.m. at Mission Boulevard and Cherry Way and will be booked at the Alameda County Jail in Dublin.
She had narcotics on her person, he said.
A man who was crossing the street with the woman was killed in the crash, Sherry said.
The deputy, a nine-year veteran of the sheriff's office, was not injured, according to Sherry.
CHP investigators interviewed the deputy because he was a key person in the incident and authorities are trying to determine what he was doing at the time of the collision, Sherry said.
Alameda County Sheriff's spokesman Sgt. J.D. Nelson was unavailable for comment on the incident.
Authorities are not yet releasing the names of the man and woman who were struck by the deputy.