Officers were called to an address in Woodhurst Road in the Moseley area of Birmingham at 11pm on Wednesday, West Midlands Police said.
Soon after arrival they found a 27-year-old man with stab wounds.
He was taken to hospital, but died on Thursday morning.
A 43-year-old man was initially arrested at the scene on suspicion of attempted murder, while the injured man was still alive.
He remains in police custody, the force said.
Meanwhile, a forensic examination of the address is being carried out and officers are going door-to-door, speaking to neighbours.
Detective Inspector Michelle Allen, from the force's homicide unit, said: "We are in the early stages of our inquiry, but we will be questioning the man in custody today."