The Irishman hit a hairpin on the race's queen stage much too fast, and was unable to stop before smashing into a car that was taking the same turn ahead of him.
Brammeier, who joined the South African team this year, later tweeted a photo from hospital to let people know he was OK, despite suffering broken ribs, a fractured pelvis and a punctured lung.
MTN-Qhubeka team doctor Jarrad van Zuydam said: “Thankfully, Matt has suffered no head, neck or spinal injuries and is currently stable in hospital. His musculoskeletal injuries are significant, however.
“He suffered rib fractures on both sides as well as a small pneumothorax. He also has fractures of the sacral and pelvic bones. Matt is unlikely to require surgery but will need some time to recover from his injuries.”
Spectator Aaron Cengiz managed to film the awful crash and later spoke to local news outlet Fox 13 Salt Lake City.
“Man he could’ve died, you know?” Cengiz told the station. “As hard as he hit that car, he could’ve died.”