The 34-year-old was sin binned for his actions during the first half of the match at Stadio Olimpico on Saturday.
He lifted his right leg and brought it down on the chest of Favaro.
It is only the second time O'Driscoll has been sent to the sin bin in his 14-year professional career, but he was lucky to have escaped a red card for the incident.
An independent Six Nations disciplinary committee convened in London on Wednesday decided the offence was in the mid-range of severity, but deducted two weeks on account of his "exemplary previous playing and disciplinary record".
It means he will miss Leinster's Amlin Challenge Cup quarter-final against Wasps on 5 April.
His ban expires three days later, making him available for the latter stages of the RaboDirect PRO12 title push.
It is thought O'Driscoll was acting out of frustration, as Ireland slumped to their first Six Nations defeat against the Italian side.
Saturday's game was potentially O'Driscoll's last with the Ireland team as his contract expires in the summer, it is speculated his forthcoming tour with the British & Irish Lions will be his farewell.