Officers broke into the apartment at around 5.30am after neighbours alerted them to an argument inside the home, according to the Rheinische Post (RP).
Once inside, police found a 3-year-old girl and a 39-year-old woman, both of whom were already dead.
In a further room, police came across a man and an officer fatally shot him.
“It came to a confrontation. We can’t say more at this stage,” a police spokesman told RP.
The deceased are believed to be a husband and wife and their daughter.
“A lot points to this being a fight within the family,” the spokesperson said.