Eight people on the KNM Helge Instad were injured in the 4am collision said Rear Adm. Nils Andreas Stensoenes, the head of Norway's navy.
The tanker, the Sola TS, was slightly damaged and it appears that it did not spill oil.
"Due to the damage to the frigate it was moved to a safe place", Nato's Allied Maritime Command said in a statement. The coastal water where the stricken vessel lies is normally prone to heavy seas, but unseasonably calm conditions prevail.
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.
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 Norwegian Accident Investigation Board, the Defense Accident Investigation Board and the Maltese Marine Safety Investigation Unit are all investing the incident.
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.
"A small oil slick from the frigate has been detected, but nothing large", the official added.
Production at a number of surrounding North Sea oil and gas facilities was temporarily stopped after the collision as a precautionary measure but has now resumed.
"It took on a lot of water and there is a real danger that it sinks where it is", a rescue official told AFP. He declined to comment on what would happen to the weapons on board the ship.
The 134-meter (442-foot) long frigate, built in Spain in 2009, has a helipad platform on its stern.
A Norwegian frigate collided with an oil tanker in the dark on her way home from the largest North Atlantic Treaty Organisation war game since the end of the Cold War.