The Belgian won the individual time trial and the road race at the Paris Olympics and won the best young rider's jersey at the Tour de France in July.
Evenepoel's father, Patrick, told Belgian media he was as yet unaware of his son's condition as he rushed to be with his son at a hospital in the capital.
"Remco was transferred to the Erasme hospital in Anderlecht (in Brussels). We're still waiting to see how he's doing. We're on our way to the hospital," he told daily newspaper Het Laatste Nieuws.
Evenepoel successfully defended his world time-trial title in Zurich in September and is a former winner of the Vuelta a Espana.
Later in a statement, his road trade team Soudal Quick-Step said that the Belgian had "sustained fractures to his rib, right shoulder blade and his right hand".
"Remco has pain in his shoulder and his hand. Our doctor is working on it," Soudal-QuickStep's manager Patrick Lefevere told Belgium's state-funded sports website Sporza.
"His bike broke in two in that incident. But it's better to split his bike in two than his arm."