Blues second row Williams was found guilty of stamping by a SANZAR judicial committee on March 22 after being sent-off by referee Paddy O'Brien for vigorously rucking near Crusaders flanker and All Blacks team-mate Richie McCaw's head in their Super 12 match on March 19.
The appeal committee of chairman Jannie Lubbe SC (South Africa), John Freedman (Australia) and Chris Morris (New Zealand) upheld the original decision meaning Williams will miss all rugby up to and including May 3.
Team-mates David Gibson and Sam Tuitupou were banned for two weeks for their part in the incident but decided against appealing.
The Blues play defending champions ACT Brumbies this weekend.
Williams will also miss games against the Cats, Sharks, Stormers and Bulls.