The issue with the corvette-class ship "Emden" was found during an inspection at a shipyard in the northern city of Hamburg, said the Sueddeutsche Zeitung daily and the broadcasters NDR and WDR.
The warship, which was slated for deployment in the Baltic Sea, had not yet been delivered to the German navy when the discovery was made.
The presence of the metal shavings could have caused considerable damage to the ship if it had not been spotted in time, said the report.
The incident on the Emden was now being investigated by the Hamburg regional prosecutor's office and the local criminal police, the report said.
The prosecutor's office and police declined to comment when contacted by AFP, and the defence ministry in Berlin did not immediately respond to a request for comment.
The German navy has ordered a total of five corvette-class ships, including the Emden, and tasked Naval Vessels Luerssen with construction. A spokesman for the shipyards said the Emden had recently completed "a succesful sea trial" but declined to comment further.
The circumstances of the incident were not immediately clear, but Germany has been on high alert to the risk of sabotage and other so-called hybrid attacks, which do not use conventional military tactics.
Along with its partners in the NATO military alliance, Germany suspects that Russia has launched undercover action against western countries as it pursues its invasion of Ukraine.
Earlier this month, police said they were investigating drone sightings over an air base in the north of Germany where Ukrainian forces are trained.
The incident was the latest in a series of drones spotted over military and industrial sites in Germany in recent months that have caused alarm.
Likewise, the Baltic Sea in particular has seen a large number of suspected hybrid war incidents, including the cutting of undersea cables connecting NATO members.
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