Moore, 25, came up short during a back flip while competing in the snowmobile freestyle final Thursday, CNN reported Tuesday. The front skis of the vehicle clipped the ground and Moore flew forward over the handlebars.
The 450-pound snowmobile hit Moore and tumbled over him as the athlete slid down the hill, CNN reported.
The snowmobiler was taken to St. Mary's Hospital, where family has gathered, The Denver Post said.
Moore's grandfather, Charles Moore, said his grandson is in dire condition.
"Caleb is not doing good at all," he said Monday afternoon. "The prognosis is not good at all. It's almost certain he's not going to make it."
He was initially taken to Aspen Valley Hospital with a concussion when doctors discovered internal bleeding around his heart. He was taken by helicopter to St. Mary's for further treatment. The heart ailment led to "a secondary complication involving his brain," a family spokesman said.
"The Moores want to express their gratitude to all of Caleb's fans, friends and family for their strong support and ask for continued prayers in the coming days," Moore's family said in a statement.
Moore's brother, Colten, also was injured Thursday while competing at the X Games though his specific event was not reported. He was released from the hospital Saturday, CNN said.
Colten Moore encouraged fans to pray for his brother in a Facebook post.
"We continue to fight and pray for him," he wrote.