Berghan was red carded in the early stages of Edinburgh's 18-17 Pro14 win over Glasgow Warriors on Saturday after his boot made contact with the head of international team-mate Fraser Brown.
He will miss the return clash with Glasgow, a league meeting with Southern Kings and the European Challenge Cup double header against Stade Francais.
The forward's ban expires on February 4, rendering him unavailable for Scotland's trip to Cardiff the preceding Saturday.
Berghan made his international debut against France in February and has five caps to his name.
Photo Getty Images. Caption: Edinburgh and Scotland prop Simon Berghan