The ship, the MV Longchamp, was attacked and boarded by seven pirates early Thursday in the pirate-infested Gulf of Aden, German public broadcaster Deutsche Welle said. It cited the vessel's Hamburg-based owner, Bernhard Schulte.
The vessel was on its way from Norway to Vietnam when the pirates attacked.
The 12 Filipino and one Indonesian crew members aboard apparently exchanged fire with the pirates, who then overpowered the crew, Deutsche Welle said.
The Longchamp had been steering in a corridor secured by Western military vessels and sent a distress signal that was caught by British forces. However, they arrived too late at the scene.
The ship's captain was able to call his owner; he said all crew members are fine. So far, the kidnappers demanded no ransom.
The Longchamp is the third ship kidnapped in the region this year, despite a large presence of Western military vessels in the Gulf of Aden, an area of 1 million square miles bordered by Somalia and Yemen.
Piracy has taken a heavy toll on international shipping: Last year pirates hijacked a Saudi supertanker carrying some 2 million barrels of oil valued at more than $100 million.