Emergency services were called to a block in the northern Berlin district of Wedding at around 8:30am, after a neighbour reported seeing a seriously injured man lying in the courtyard.
The police arrived to find an open window in a fourth-floor flat, where they discovered the body of 21-year-old Hannah K. lying in the living room.
"After investigating the flat, officers came upon a dead woman with several stab wounds," a police spokesman told the Bild newspaper.
The victim, described as a freelance artist who had studied textile and surface design, is said to have rented the 160-square-metre flat two months ago, and sub-let the other rooms to five men.
The motive behind the killing remains a mystery – the man is still unconscious and severely injured in hospital.
"The perpetrator and victim were not apparently romantically involved," the spokesman said.