The crash involving a Honda Civic and Toyota Camry was reported on Osgood Road between Blacow Road and Auto Mall Parkway around 12:15 a.m., Sgt. Tony Tassano said.
A 33-year-old woman of Fremont was driving a silver Civic south on Osgood Road when she veered onto northbound lanes and slammed head on into a silver Camry, Tassano said.
The woman had her 4-year-old daughter buckled into a car seat that was not properly secured to the vehicle, he said.
The woman was listed under critical condition but as of about 4:30 a.m. was upgraded to stable condition, Tassano said.
Her 4-year-old daughter sustained life-threatening injuries, he said.
Officers said they could smell alcohol on the woman at the scene, according to Tassano.
A witness told police the woman was driving about 50 to 60 mph prior to the crash, he said.
The driver of the Camry, a 30-year-old man of Fremont, sustained minor injuries to his legs and was transported. The man told officers that he had been drinking alcohol before he drove, Tassano said.
The road was reopened at about 6:45 a.m., he said.