"Upon entering the apartment, officers discovered the partly dismembered body of the 30-year-old tenant and detained the 32-year-old husband after he attempted to resist them," police said in a statement.
A police spokesman said later that the body parts were discovered on the terrace of the flat and that limbs had also been found in the courtyard of the building. An autopsy showed the woman had been stabbed to death.
The man, who is believed to work in the building industry and who, authorities say, has several traffic violations and tax infractions on his police record but no violent crimes, was to appear before a judge later Monday.
Neighbours alerted the authorities after hearing loud noises from the apartment in the early morning.
The six children, who were apparently unscathed, were handed over to social services, police said.
They were not able to say whether all six, who are between the ages of one and 13, two girls and four boys, belonged to the couple.
A witness told local public radio station RBB that she had seen the man, who she said was Turkish, on the roof of the five-storey apartment building holding up the head of the woman in one hand and a knife in the other.
Her mother saw him throw the head into the courtyard, she said. She said she had earlier seen the man strike and kick his wife.
The Berliner Morgenpost newspaper reported in its online edition that the children were in a room with the door closed at the time of the killing and did not see what occurred.
But other neighbours told German news agency DPA that they could see the children looking out the window as the murder took place.
One said that the man had had another lover living in the building with whom he had two children and that the wife had previously thrown her husband, with whom she often fought, out of the apartment.