The 17-year-old boy was arrested at an address in Netherton, West Midlands Police said, and remains in custody.
A 65-year-old man was attacked at 18:15 GMT in Owen Street, Kates Hill, Dudley, suffering serious stab wounds to his head, shoulder, chest and back.
Police said he was now in a stable condition in hospital.
Det Insp Greg Evans said: "Thankfully, the man is... recovering well in hospital.
"We are still working to establish a motive for the attack and we are currently questioning a teenage boy, who was arrested yesterday afternoon."
A teenager has been arrested on suspicion of attempted murder after a man was stabbed on his doorstep in the West Midlands on Tuesday.