Fairfield police say 18-year-old Joshua Cooper was being held Friday in the Solano County Jail on suspicion of child cruelty and aggravated mayhem.
Police say they received a call Thursday by a distraught woman who said her baby was bleeding from his nose.
Doctors later determined the child suffered a skull fracture, a brain hemorrhage and that one third of the child's nose had been severed.
The child is in stable condition at Oakland Children's Hospital.
Police say they are still trying to determine how the skull fracture and brain hemorrhage occurred.