The 27-year-old committed the offence in the Blues' Heineken Cup defeat against Northampton last month and will be suspended until March 31.
Rees' ban has left the Blues in dire straits with only one specialist scrum-half available to boss Dai Young in the shape of Tom Slater.
And Wales boss Warren Gatland will also be less than impressed with the punishment.
Gatland has found himself under increasing pressure going into the Six Nations campaign following a dismal autumn in which a draw, against minnows Fiji, was their best result.
Rees had established himself as a more-than-capable No. 2 to first-choice half-back Mike Phillips and with his prololonged absence the door may be open for a return for Sale Sharks scrum-half Dwayne Peel.
Peel has been a victim of Gatland's policy of only picking domestic-based players but the Kiwi may now have his hand forced for the Six Nations which kick off against England on February 4.