Oxnard Police Sgt. Randy Latimer says the truck struck 19-year-old Alma Lopez Tuesday morning in a crosswalk, knocking her to the ground.
The truck continued on, dragging the children - a 3-year-old girl and a 1-year-old boy - and the stroller until witnesses chased and flagged down the driver.
Latimer says the driver, Mehran Khamseh of Santa Barbara, was arrested on suspicion of driving under the influence of drugs.
The children are hospitalized in critical condition. Lopez's injuries were described as moderate.