Up to eight people were injured in the collision in the Hjeltefjord near Bergen, Norway, when the KNM Helge Ingstad crashed into a vessel from Malta.
The KNM Helge Ingstad frigate has been listing dangerously.
There were no reports of damage or leaks from the oil tanker, identified as Sola TS.
One Norwegian news outlet reports that according to tracking data, the frigate's geolocation system was turned off at the time of the collision, noting, however, that the armed forces of Norway have neither confirmed nor denied that. The coastal water where the stricken vessel lies is normally prone to heavy seas, but unseasonably calm conditions prevail.
Eirik Walle, of Norway's rescue centre, told Norwegian news agency NTB the collision smashed a hole in the side of the warship.
Some 10,000 litres of helicopter fuel from the frigate's tanks leaked into the sea, Johan Marius Ly of the Norwegian Coast Guard said.
The shipping site Sysla said the tanker had been loaded with crude oil and was being towed out of the harbor when it somehow rammed the frigate.
"A small oil slick from the frigate has been detected, but nothing large", the official added.
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No oil spill has been reported from the tanker, which was sailing from Equinor's Sture terminal in Øygarden.
"It took on a lot of water and there is a real danger that it sinks where it is", a rescue official told AFP.
"The KNM Helge Ingstad suffered damage above and below the waterline".
The 134-metre long frigate, built in Spain in 2009, has a helipad platform on its stern. The warship was launched in November 2007.
It had recently taken part in NATO's large-scale Trident Juncture military exercises, where it was engaged in submarine hunting maneuvers.
An image of the ship tipped to one side was posted with the comment.