The 19-year-old is recovering in an Italian hospital after tangling with another rider and hitting a bollard.
Yee, who is due to sit A-Levels this week, is undergoing concussion checks.
Also a gifted track athlete, last week he set the fastest 5,000m time by a British junior since 1981.
Yee, from Brockley, London, was last year tipped by Mo Farah as a future Olympian.
In a statement, British Triathlon said Yee had briefly lost consciousness after the crash.
"Alex is receiving a very high level of care and it is hoped that he will be able to return home in the next few days," the statement added.
British triathlete Alex Yee suffered broken ribs, vertebrae and a collapsed lung in a high-speed bike crash during an ITU Triathlon World Cup event in Cagliari in Italy on Sunday.