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 warship is currently in danger of sinking, named the Sola TS, is slightly damaged and did not spill oil.
3am (4am local time) during a training session, officials have confirmed.
The tanker had a sail from Equinor's Sture.
Nato's Allied Maritime Command said in a statement: "Two to the damage to the frigate."
The tanker, which was carried to a crew of 23, was returned to port for an inspection.
It is unclear what caused the collision but several oil and gas terminals were shut down as a precaution.
These include the Sture export oil terminal, the Kollsnes gas plant and several offshore oilfields.
The Sture terminal sees more than 25 percent of Norway's oil production going through the facility, while the Kollsnes plant processes gas for a number of EU member states as well as the UK.
A source told AFP news agency to "small oil slick" was detected from the warship and that "it took a lot of water and there is a real danger that it sinks where it is".
Twitter users are waiting to see if the huge vessel sinks while uploading images onto social media.
One said: "The situation is going to be worse for Norwegian frigate #HelgeIngstad."
A picture of the ship was posted with the comment.
It can take a long time to sink into the water.
The KNM Helge Ingstad frigate was launched in November 2007 and measures 134 meters long.