The Simushir cargo ship is carrying hundreds of tons of fuel, prompting fears it could run aground and cause a spill along the pristine coast.
A Canadian ship is now towing the vessel away at a speed of 1.5 knots.
It had been thought the ship might hit Haida Gwaii, known as the Queen Charlotte Islands.
Further bad weather is expected and government officials say preparations are being made in the event of a fuel spill.
A nearby First Nation community said that would be a "catastrophic event".
The Canadian coast guards' ship the Gordon Reid arrived late on Friday. A tugboat is set to join both vessels early Saturday morning and help tow the Simushir to Prince Rupert, British Colombia.
Sub Lt. Melissa Kia of Canadian Forces Base Esquimalt said three more vessels, including a US coast guard ship were also on their way.
The ship, with a crew of 11, lost power early on Friday morning as it made its way from the US state of Washington to Russia.
The captain was rescued by a Cormorant helicopter because he was injured.
Memories of oil spills loom large in British Columbia, where residents remember the Exxon Valdez oil spill of 1989.
Canadian coast guards have attached a tow line to a Russian container ship drifting without power in rough seas off British Columbia.