The crewman who died suffered a head trauma while exiting the boat and was already deceased when rescuers arrived, but it's not clear if he died from the injury or hypothermia, said Dr. Phil Hess at Cordova Community Medical Center in Cordova, Alaska.
The three men and one woman were in the frigid water at least two hours before a Coast Guard helicopter rescued them, he said.
The rescue was caught on tape, as were distress calls from the boat.
The three who survived suffered hypothermia, but were in stable condition late Tuesday because they wore protective gear, Hess said.
An HC-130 Hercules aircraft arrived before the chopper did and dropped a life raft and the survival gear. The helicopter was from Air Station Kodiak.
"It's cold. They were wearing survival suits, which gave the other three the chance they had and they're doing well," Hess said.
Hess declined to give details of the injured because family members had not been notified but said the deceased was a man.
The crew of the Northern Belle sent a Mayday radio call at about 5:30 p.m. local time that the boat was sinking about 50 miles south of Montague Island, said Coast Guard Petty Officer 1st Class David Mosley. That's near the mouth of Prince William Sound.
"We are going down," one of the male crew members told a Coast Guard dispatcher, according to an audio recording of the distress call that accompanied a news release from the agency.
The operator of the boat, Robert Royer, was among the crew, Petty Officer Jeffrey Roberto from the Coast Guard's Juneau office told The Seattle Times.
Records show the fishing boat is owned by Triton Inc., Roberto said.
CBS News' Tara Mergener's report on the rescue included the riveting video, and audio of the distress calls from the sinking boat: