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.
Helge Ingstad took on water and all 137 personnel were evacuated, according to the statement, which added that eight suffered minor injuries.
The tanker, the Sola TS, was only slightly damaged and it appears that it did not spill oil.
One said: "The situation is going bad to worse for Norwegian frigate #HelgeIngstad". The collision tore a large hole in the hull of the vessel, which began taking on water and had to be pushed into shallow coastal waters by tugboats to keep it from sinking.
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 two vessels collided at about 04:00 local time (03:00 GMT) as the frigate was sailing inner fjords for training, officials say.
The Sture terminal is a major tanker port, with nearly 25% of Norway's oil production passing through the facility.
Norway's largest oil and gas company Equinor, formerly known as Statoil, said it shut down non-emergency activities at the Sture terminal where the collision occurred "as a precautionary measure". The Norwegian Accident Investigation Board, the Defense Accident Investigation Board and the Maltese Marine Safety Investigation Unit are all investing the incident.
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A small oil slick has surrounded the ship following the collision.
The 62,000-tonne tanker received only slight damage and is waiting to be towed to a nearby oil terminal, the rescue centre official said.
The Helge Instad is 442 feet long and was built by Spanish shipbuilder Navantia in 2009.
"It took on a lot of water and there is a real danger that it sinks where it is", an official for the Sola rescue centre told AFP.
The Trident Juncture 18 live drills concluded on November 7 in Norway.
The frigate had recently taken part in a North Atlantic Treaty Organisation exercise.
The ship had previously been part of an escort convoy which seized chemical weapons from Syria back in 2013.