Briggs will be sidelined for the Exiles' Amlin Challenge Cup fixtures against Cavalieri and Stade Francais, plus their LV= Cup appointment with Harlequins.
Briggs was reported by independent citing officer John Byett for punching or striking Smith during last Sunday's Aviva Premiership game at the Kassam Stadium.
The Rugby Football Union disciplinary panel were also due to consider a citing against England and Leicester fly-half Toby Flood for an alleged tip tackle on Worcester opposite number Andy Goode.
