The woman, whose name is not being released, got in an argument with her husband at about 2 p.m. Thursday, according to Union City police. She allegedly attacked him with a knife and cut his arm.
The husband, whose name is being withheld at his request, went to a local hospital for treatment and did not call the police.
When he returned, he found that his 7-year-old and 10-month-old daughters had been cut. He called police, and when officers arrived, they found his wife sitting on the porch and looking distraught, according to Union City police.
The girls were taken to Children's Hospital in Oakland, police said. The 7-year-old is stable, but the 10-month-old needed surgery. Her condition was not immediately available.
The mother was taken to a local hospital for evaluation. Police said they are still investigating the case and considering various criminal charges.