The girl was taken in a Jeep Liberty at about 6:40 a.m. in the 2300 block of Amador Court, off of Story Road, a few blocks from Interstate Highway 680.
The mother, Graciella Quintera, had placed her 11-month-old daughter Gabriella in a car seat in the backseat of the Jeep but had not yet strapped her in, San Jose police Sgt. Jason Dwyer said.
Quintera was bringing items from her house to her car and stepped away from the Jeep momentarily, leaving the key in the ignition with the engine off, Dwyer said. When she came back outside she saw the Jeep driving away.
Her daughter, whose first birthday is in four days, was gone, police said.
She called police, who arrived within three minutes, Dwyer said.
Quintera, who is a single mother, did not recognize the suspect but saw her standing nearby before the car was stolen, Dwyer said.
"The mother is understandably shaken," Dwyer said. "It's very difficult to interview someone in that condition."
San Jose police said they don't know if the motive was to steal the car or the baby.