The tug boat Stevns Power went down with six Filipinos, three Danes and two Congolese aboard, according to a report on Danish state television.
The incident occurred when the Stevns Power was working with other support ships alongside the world's largest ship for laying pipelines and erecting floating cranes, the Castro Otto, in the oil-rich waters of the Gulf of Guinea.
The tug had been dropping anchor when it capsized without warning and sank in 80m of water, according to the Danish reports.
Nigerian authorities say the weather was fine at the time and the wind was blowing at a moderate 10kms per hour.
Built in Denmark in 1976, the 40 metre (130-feet) vessel is owned by Nordane Shipping in Svendborg, a small town 165km southwest of the capital, Copenhagen.
Shipowner Niels Hoejlund of Nordane Shipping told the regional Danish daily Fyens Stifstidende: "I can't understand why no crew member was able to get off the ship, which sank suddenly for as-yet unexplained reasons."