Investigations will now confirm whether the saw is connected to the death of Swedish journalist Kim Wall, reports the Ritzau news agency.
Copenhagen Police confirmed in a press statement that the saw was found on Wednesday, close to the route sailed by the vessel on August 11th.
The implement will be examined by forensic experts to ascertain whether it was used to remove Swedish journalist Kim Wall's head, arms and legs from her body.
"The saw is now being examined by our forensic technicians to assess whether it is the saw police have been looking for in connection with the submarine case," lead investigator Jens Møller Jensen said.
Earlier this week, Madsen announced through his lawyer that he no longer wished to answer police questions in connection with the case.
That came after a weeks-long police search resulted on Saturday in the discovery of 30-year-old Kim Wall's missing clothes, her head and legs, and a knife in Køge Bay south of the Danish capital.
Madsen denies both killing Wall and improper conduct with her body and has previously claimed that she died after being accidentally hit by a hatch on the submarine.
No signs of cranial fracture were found on Wall's head.