The plane went off the right side of the runway, flipped over and burst into flames on Sunday afternoon, said Alex Burchetta, director of operations for the Pitkin County Sheriff's Office.
The airport remained closed as authorities investigated the crash during the busy ski season.
Miguel Henriqez was in critical condition and Moises Carranza was in serious condition at St. Mary's Hospital in Grand Junction, spokeswoman Kimberly Williams said.
Both are pilots and one was co-piloting the plane with Sergio Carranza Brabata, also of Mexico, who died in the crash. It was not clear who was in control of the plane when it went down.
Quick action by airport fire crews to extinguish the flames probably saved the lives of the two survivors, Pitkin County Sheriff Joe DiSalvo said.
No one else was on board. The National Transportation Safety Board was investigating to determine the cause as wreckage remained on the runway.
Authorities said investigators must examine the debris before it can be moved. In addition, authorities were awaiting the arrival of representatives of the airplane manufacturer.
Meanwhile, airlines were busing travelers to the Denver and Grand Junction airports. Assistant aviation director Brian Grefe said about 3,000 travelers had been affected.
Officials say the flight originated in Mexico and stopped in Tucson, Ariz., before heading to Aspen, where landing is challenging because of surrounding mountains that require pilots to descend sharply.
In 2001, 18 people died when a chartered Gulfstream III jet from Burbank, Calif., hit a hillside just west of the airport.
At least two celebrities — LeAnn Rimes Cibrian and comedian Kevin Nealon — saw the crash and tweeted about it.
Rimes Cibrian tweeted via @leannrimes on Sunday: "So sad! Horrible plane crash we just saw happen at the Aspen airport."
Nealon sent a series of tweets about the crash through @kevin_nealon.
His first one said, "Horrible plane crash here at Aspen airport. Exploded into flames as it was landing." Later he tweeted, "Airport is closed now. I think I'll drive back to LA after seeing that."
The plane was a Canadair CL-600, a midsized private jet, said Peter Knudson, a spokesman for the NTSB. Records indicate it is registered to the Bank of Utah in Salt Lake City.
Bank officials did not immediately respond to phone and email messages seeking comment.
A plane with the same tail number took off at 6 a.m. MST from the airport in Toluca, a city 35 miles west of Mexico City, before stopping in Tucson, according to a Mexican federal official who spoke on condition of anonymity because he was not authorized to speak to the press.
Snow showers were reported in the area Sunday afternoon, but not at the airport, said Tom Renwick, a National Weather Service meteorologist in Grand Junction. He said it has been overcast all day with temperatures hovering around 10 degrees.
Aspen is located in the Rocky Mountains about 100 miles southwest of Denver.
Associated Press writers Jake Coyle in New York and Adriana Gomez Licon in Mexico City contributed to this report.
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