Sola TS tanker crashed into Helge Ingstad, tearing a large hole in its side, near the Sture terminal in Oygarden at around 4 a.m (0300GMT) on Thursday.
The frigate was taking a lot of water and seven of its crew were injured, police told the newspaper, adding that everyone aboard the vessels has already been evacuated.
Rear Admiral Stensoenes said the frigate had been pushed by towboats into shallow waters where it could not sink fully.
Some 10,000 liters of helicopter fuel from the frigate has leaked into the sea, said Johan Marius Ly of the Norwegian Coast Guard.
The Sture Oil Terminal processes about 500,000 barrels a day of North Sea oil, including oil from the Ivar Åssen, Grane and Edvard Grieg fields.
It is planned that the tanker will return to the dock for an inspection.
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Sola TS was loaded with crude oil and was heading to Britain.
He would not confirm further details as reported by a Norwegian defence and security website, which broke the news that the two vessels could see each other and followed communication protocols on an open channel.
Norway's Accident Investigation Board, which has opened an inquiry, had initially said a tugboat had also been involved in the collision but the Navy later denied that. Launched in 2007, the warship is named after the famous Norwegian Arctic explorer. The next part - a command post exercise - will be held from November 14 to 24.
The ship was returning to the Haakonsvern Naval Base near Bergen after the military exercises, officials said. Norway has grown increasingly nervous about neighboring Russian Federation since it annexed Crimea from Ukraine in 2014.
The Norwegian Armed Forces are leading the recovery operation in close co-operation with the Norwegian Coastal Administration.