Fred Jackson, 46, was arrested after the stabbing was reported at 12:02 a.m. Monday at a home on Orion Court, Alameda police Lt. Sean Lynch said.
Officers responded and found the 26-year-old woman, Jackson's former girlfriend, had suffered a 1-inch vertical laceration to her face. She was taken to a local hospital, Lynch said.
The infant was unharmed, he said.
Jackson, who said he is a transient, has a history of domestic violence with the woman, who had filed a restraining order against him. Nevertheless, she let him stay for the evening at the house, which she now shares with another boyfriend, according to Lynch.
He allegedly waited until the victim was asleep and then "essentially attacked her unprovoked," Lynch said.
When officers responded and arrested Jackson outside the home, he "declared his intent was to kill her, to kill her in her sleep, and said he'll finish the job when he gets out of jail," Lynch said.
Jackson was arrested on suspicion of attempted murder, making criminal threats, child endangerment and violating the restraining order, according to Lynch.