The launch of the balloon had been delayed several times due to strong winds. Baumgartner had entered a capsule he was to ride in -- suspended from the balloon -- just before 11 a.m. MDT, before the mission was aborted for the day, Fox News reported.
Baumgartner had said prior to the attempt he was nervous about jumping from an altitude of nearly 23 miles, but he said that's a good thing.
"Having been involved in extreme endeavors for so long, I've learned to use my fear to my advantage," Baumgartner, a 43-year-old former military parachutist, said in a statement.
"Fear has become a friend of mine," he said. "It's what prevents me from stepping too far over the line."
Baumgartner, who has been preparing to attempt to break the world record for highest-ever skydive, had been scheduled to lift off in a 55-story helium-filled balloon at 6:57 a.m. MDT. Winds must not exceed 2 mph at liftoff to ensure the balloon -- whose material is 10 times thinner than a plastic sandwich bag -- isn't damaged, officials of the Red Bull Stratos mission said.
The ascent to 120,000 feet, when it eventually occurs, could take as long as 3 hours, officials said. When Baumgartner reaches the right altitude, he will jump from the capsule and plummet to Earth in a harrowing free fall that will make him the first skydiver to break the sound barrier.
If he does, he would also break a record set in 1960 by Joe Kittinger, who jumped from an open gondola 19.5 miles up but came just shy of breaking the sound barrier.
Kittinger -- who is now 84 but was a 32-year-old U.S. Air Force captain at the time -- reached a speed of 614 mph, The (Oklahoma City) Oklahoman reported.
Kittinger now serves as a Red Bull Stratos adviser, Space.com said.
The mission was to have been streamed at redbullstratos.com, with a 20-second video delay of the jump in case of a tragic accident.
Baumgartner's jump is not just for thrills, officials said.
Among the mission's advisers is Dr. Jonathan Clark, a former NASA flight surgeon whose wife, astronaut Laurel Clark, died in the 2003 space shuttle Columbia disaster.
Clark is dedicated to improving astronauts' chances of survival in a high-altitude disaster, The Oklahoman said.
"Red Bull Stratos is an opportunity to gather information that could contribute to the development of life-saving measures for astronauts and pilots -- and maybe for the space tourists of tomorrow," Baumgartner said in his statement.
"Proving that a human can break the speed of sound in the stratosphere and return to Earth would be a step toward creating near-space bailout procedures that currently don't exist."