Trooper spokeswoman Megan Peters said the aircraft went down Saturday night, the wreckage spotted Sunday, and no survivors have been found.
Peters said that though the three are feared dead, there has been no confirmation of any fatalities.
"This is a huge, profound tragedy for us. We can replace the helicopter but we can't replace what went down with it," she said. "It's been a bad day."
Wreckage of the helicopter burned, but Peters said it was not known how the fire started or how long it lasted.
The trooper helicopter was on a mission to pick up a snowmobiler stranded near Larson Lake 7 miles east of Talkeetna in the Matanuska-Susitna Borough.
The helicopter picked up a trooper and began a search, spotting the snowmobile and landing just before 10 p.m. It took off with the snowmobiler and was supposed to meet medics near Talkeetna but did not arrive.
The National Weather Service said the temperature in Talkeetna Sunday night was 34 with light rain that turned into snow at about 11 p.m., but that visibility was 10 miles.
Peters said it's not known if weather was a factor in the crash. The National Transportation Safety Board will investigate.
Alaska Air National Guard helicopter spokeswoman Kalei Rupp said fog in Anchorage and mandatory crew rest kept an agency helicopter from launching until 5 a.m.
A guard helicopter spotted the wreckage at 9:20 a.m. Sunday and landed.
Talkeetna is a community of nearly 900 about 80 miles north of Anchorage. It's the primary departure point for air taxis taking climbers to Mount McKinley.
The crash site was near the south end of Larson Lake.
The Alaska State Troopers have had at least one officer die in a helicopter crash during a search and rescue mission.
Trooper John David Stimson was on a chartered helicopter in 1983 that was attempting to reach a downed pilot in a blizzard. The chartered helicopter crashed near Cordova.
Stimson survived and assisted pilot Gary Wiltrout, who had suffered a broken back. However, when rescuers reached the crash site after 24 hours, the 11-year trooper had died of exposure. Wiltrout survived.
AP writer Bob Seavey in Phoenix contributed to this story.