The arrested suspect is a 45-year-old man. He had come to the scene for a scheduled conversation about custody of his daughter, Focus reports after the police press conference on Monday evening.
Four women and two men were killed.
"The perpetrator was arrested in a car immediately after a police chase, and a firearm was found in the vehicle," the Lüneburg police wrote in a statement.
A 65-year-old woman has also been arrested. She is believed to have driven the getaway car and, according to police, had close ties to the family. The daughter's mother has also been arrested.
The area at the crime scene will remain closed on Tuesday, police said.
