Although the tanker was undamaged, the £465 million frigate took on large quantities of water and was in danger of sinking when the captain took her into shallower water before running her aground.
The Maltese-flagged tanker, Sola TS, was not damaged and its 23-man crew remained on board.
Norwegian news agency NTB is reporting that the collision tore a hole in the frigate's side, and that it is taking in more water than can be pumped out. The coastal water where the stricken vessel lies is normally prone to heavy seas, but unseasonably calm conditions prevail.
It was being towed out of the harbour when it somehow managed to ram the frigate.
Comment: Again, laden massive cargo ship collided with Navy frigate, similar to accidents which occurred with USA Nay frigates in Japan and off Singapore, recently.
Norway has been forced to close the Sture Oil Terminal near Bergen and has started closing down the nearby Kollsness gas-and-condensate terminal - a lifeline of heating gas to Europe - after an early morning collision between a $440-million frigate and an oil tanker.More news: Meg Ryan announces engagement to John Mellencamp
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The Navy quickly evacuated all the crew except for 10 essential staff members to prevent a possible fuel leak.
Rear Admiral Stensoenes said the cause of the accident was not clear and the Navy would wait for the findings of Norway's Accident Investigation Board.
"The KNM Helge Ingstad suffered damage above and below the waterline".
The two vessels collided at about 04:00 local time (03:00 GMT) as the frigate was sailing inner fjords for training, officials say.
Pictures show water has also overwhelmed the frigate's helicopter platform on its stern.
NATO's "Trident Juncture", the largest military exercise since the end of the Cold War, launched in Norway on October 25 and is due to run until November 7.
The ship had previously been part of an escort convoy which seized chemical weapons from Syria back in 2013.