Police were called to a house on Alfred Road, in the Handsworth area of Birmingham, at about 10.45pm on Friday night.
The baby boy had received several stab wounds and was admitted to hospital with life-threatening internal injuries but his condition had stabilised following an operation, a spokesman for West Midlands Police said.
A 37-year-old man arrested at the scene on suspicion of attempted murder remains in police custody for questioning.
The force spokesman said: “The child remains in hospital in a critical but stable condition.
“He is alive and is doing well despite various severe internal injuries.”