A 58-year-old woman and a 66-year-old man were shot at around 2.35pm in Groß-Steinrade, a suburb of Lübeck, police said.
The victims, reportedly a married couple, both died of their injuries a short while later.
After firing the shots outside the couple's home, the murder suspect fled in a vehicle.
The crime scene was cordoned off, while prosecutors, homicide and forensic officers investigated.
Police then searched for the shooter using a helicopter and at 5pm a white Renault Kangoo van was found on a dirt road in the nearby village of Badendorf.
Inside the van, officers found the body of a 59-year-old man from Thuringia. He died with a gunshot wound to the head. The weapon was found on him, police said.
“At the moment investigators believe that there is a link [between the shootings],” police said in a statement.
The Lübecker Nachrichten reported that the 59-year-old was the ex-husband of the woman who was shot. Investigations are continuing.