The 29-year-old Portugal international was cited after an incident two minutes from time in the French side's 30-23 Pool 1 defeat against Saracens in the European Champions Cup on Saturday.
Bardy attented a disciplinary hearing on in Dubin, where he pleaded guilty to striking the England international.
Independent judicial officer Simon Thomas deemed that the offence warranted a red card, but took into account Bardy's guilty plea as well as his previous disciplinary record and remorse during the hearing.
He will now be suspended until December 8 given that there is a period of two weeks in which Clermont are scheduled to play in the newly formed competition.