The 2009, 2011 and 2012 Heineken Cup winner was sinbinned for bringing his foot down on Favaro's chest just before the half-hour mark at the Stadio Olimpico as his side lost to the Azzurri for the first time since 1997.
O'Driscoll was found guilty of the offence at a disciplinary hearing in London earlier today and has been suspended until April 8.
His actions were deemed to be a mid-range offence, with the minimum ban set at five weeks.
The 34-year-old had that reduced by two weeks, however, as a result of his 'exemplary previous playing and disciplinary record', with Saturday's indiscretion resulting in just the second yellow card of a 14-year playing career.
O'Driscoll won't be available for the April 5 last-eight encounter with Wasps at Adams Park but he will be free to play if they make it through to the semi-final stages on the weekend of April 26, 27 and 28.
He will also miss Leinster's RaboDirect PRO12 games against fellow title contenders Glasgow and Ulster over the coming fortnight.