The National Park Service says it was a Fairchild C-123 registered to All West Freight Inc. of Delta Junction, Alaska.
The agency says there were three people onboard and apparently no survivors.
The plane crashed into the south-facing slope of Mount Healy within a mile of the park headquarters and about 200 yards north of the only road into the park. It went down about 3 p.m. near the eastern edge of the park, about 180 miles north of Anchorage.
The plane burst into flames on impact and started a wildland fire, which was contained at approximately one acre.
Military officials have said none of their planes were involved. Clint Johnson with the National Transportation Safety Board said there are a number of large transport planes operating in Alaska.
George Clare, of Las Vegas, said he saw the plane flying very low and slowly while he was walking toward the visitor's center near the park entrance. He thought the plane was going to land on a local airstrip, so he proceeded to the visitor's center. Within minutes, people came running in and saying a plane had crashed.
He said the crash caused a column of smoke a few miles west of the visitor's center. Fire managers estimated the fire at about two square miles Sunday evening.
The crash happened just four days after a military cargo plane crashed at Elmendorf Air Force Base in Anchorage, killing four people onboard.
The victims were Maj. Michael Freyholtz, 34, of Hines, Minn.; Maj. Aaron Malone, 36, of Anchorage; Capt. Jeffrey Hill, 31, of York, Pa., and Master Sgt. Thomas Cicardo, 47, of Anchorage. Cicardo was posthumously promoted to senior master sergeant Friday.
The four airmen were on a training mission Wednesday evening for a weekend air show at the Air Force base, which wrapped up Sunday. The C-17 crashed about a minute after taking off.