The 200m, Singapore-flagged, Japanese-owned Cougar Ace, which was carrying nearly 5,000 cars from Japan to Canada, had rolled almost on to its side.
A coast guard helicopter, two Pave Hawk helicopters, two refuelling aircraft and a C-130 aeroplane were sent to the area from the Air National Guard base in Anchorage.
A coast guard statement said: “Aside from one crew member with a broken leg, who will be taken to Anchorage for medical attention, there were no reported injuries.”
The rescued crew are to be taken to Adak Island, 370km away in the Aleutians.
Earlier on Monday, a coast guard aeroplane dropped three life rafts at the scene, but high seas shoved the rafts underneath the ship.
Rescuers then dropped an additional raft, but the crew members had taken refuge on the high side of the tilted vessel and the raft was beyond their reach.
A merchant marine ship later reached the vessel, but its crew were unable to rig a line to the Cougar Ace to keep it from tilting further.
Greg Beuerman, a spokesman for the ship owner, Mitsui OSK Lines, said the vessel contained lifeboats and rafts, but it would have been too risky for the crew to venture to the area where they were stored
Lieutenant Mara Booth-Miller, a coast guard officer, said: “Communications became difficult when the batteries in the crew’s hand-held radio began losing power.”
Sailors had to shout to the merchant ship, which relayed messages to the coast guard.
It was not immediately clear what caused the ship to list. Its crew had sent out an SOS late on Sunday.