The 27-year-old Edinburgh prop was hit with the ban by a Pro14 disciplinary panel who initially felt his fifth-minute red card in Saturday's 18-17 win over Glasgow for a stamp to the head of Warriors' Fraser Brown warranted a top-end entry-point suspension of 12 weeks.
The ban was eventually cut by half and Berghan will be available to play again on Sunday, February 4 - the day after the Six Nations game in Cardiff.
The panel revealed that the ban was reduced by 50% because of his previous good record, his decision to make an apology to the victim and the fact that no serious injury had occurred.
With Berghan's Edinburgh team-mate WP Nel also sidelined because of a fractured elbow, it is likely that coach Gregor Townsend will call on either Glasgow's Zander Fagerson or Jon Welsh of Newcastle Falcons to play at tight-head against Wales.