Adm. Nils Andreas Stensoenes, the head of the Royal Norwegian Navy, said Thursday during a news conference.
The KNM Helge Ingstad frigate took on water and was at risk of sinking.
Stensoenes said the ship was "strongly listing" - or leaning to one side - and that it had been pushed by towboats into shallow water, where it can not fully sink.
"It took on a lot of water and there is a real danger that it will sink where it is", an official for the Sola rescue centre told AFP.
The warship is now in danger of sinking, while the tanker, named the Sola TS, is slightly damaged and did not spill oil.
Coast guard deputy director Johan Marius Ly said helicopter fuel has leaked from the frigate.
The two vessels collided at about 04:00 local time (03:00 GMT) as the frigate was sailing inner fjords for training, officials say.
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The Sture export oil terminal, as well as the Kollsnes gas plant and several offshore oilfields, were shut down as a precaution but resumed operation on Thursday afternoon, Equinor said in a statement.
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 shipping site Sysla reported that the tanker had been loaded with crude oil and was on its way to the UK.
The 134-metre long frigate, built in Spain in 2009, has a helipad 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.
Aerial footage taken by Norwegian coastal administration aircraft during the day shows the frigate partially submerged sitting on her starboard side on the rocks. He declined to comment on what would happen to the weapons on board the ship.