The 22-year-old Wales international was injured as the Blues lost to the Asia Pacific Dragons in the third place play-off.
The Blues, who finished seventh in the RaboDirect PRO12 last season, have not revealed the nature or the extent of his injury.
A statement from Cardiff Blues said: "Cardiff Blues have today [Monday] announced that centre Owen Williams is to remain in hospital in Singapore after sustaining an injury at the World Club 10s.
"Williams was injured during the first half of the third/fourth play-off fixture with Asia Pacific Dragons on Sunday afternoon.
"The region would like to take this opportunity to thank fans for their messages of support for Owen. Cardiff Blues will issue further updates when they are available."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the RaboDirect PRO12.
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland