The 24-year-old is facing up to six weeks on the sidelines as he recovers from his fall on the first section of the one-day race's infamous cobbled sections.
Küng serves in the BMC team as lieutenant to Belgian Olympic champion Greg Van Avermaet.
“Stefan will be confined to a liquid diet for some time to minimise movement of his jaw but he is able to speak,” said BMC doctor Max Testa.
The weekend's Paris-Roubaix was tainted by tragedy with the fatal heart attack suffered by 23-year-old Belgian cyclist Michael Goolaerts.