The crew were evacuated amid fears the vessel would sink.
The Norwegian Navy has planned a news conference for later in the day.
According to Tu.no, seven people were lightly injured in the collision in the Hjeltefjord near Bergen in the early hours of Thursday.
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.
Norway's emergency services have confirmed the Helge Instad is sinking as there is "no control over the 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.
Update: Frigate understood to sustain stb bow hull breach with massive water ingress, she's said to develop heavy bow tilt.
Johan Marius Ly of the Norwegian Coast Guard said the 442ft frigate, which had recently taken part in the North Atlantic Treaty Organisation drill Trident Juncture, was listing, adding: "We have been told that there is a leak from the frigate".
The Maltese oil tanker was carrying about 625,000 barrels of crude, but officials said none spilled after Thursday's collision.
Update: 0700 UTC - according to latest reports frigate was taken to shallow waters to avoid sinking, water ingress is incontrollable.
Images of the frigate published online and broadcast on television showed the frigate was partly underwater and had been moved near the shore.
"We are doing everything we can to save the ship", Lieutenant Colonel Ivar Moen told AFP. The KNM Helge Ingstad frigate has been listing dangerously.
It is armed with ship-to-ship missiles, torpedoes and machine guns.
The warship had been returning from North Atlantic Treaty Organisation military exercises.
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.