Fellaini and Everton accepted the charge, little surprise considering the player had already apologised and his manager David Moyes also condemned the incident.
The ban is the equivalent of what the 25-year-old would have received had referee Mark Halsey seen the incident at the Britannia Stadium and issued a red card.
Fellaini will now miss Everton's Christmas fixtures against West Ham, Wigan and Chelsea.
A statement from the FA also referred to two other clashes between Fellaini and Shawcross at the Britannia Stadium but Halsey has confirmed he saw both and did not consider them violent conduct.
Fellaini's absence will be sorely felt by Everton after an inspirational first half of the season.
The Belgium international has scored eight goals and been the driving force of a team currently fifth in the table.
The FA's statement read: "The FA has charged Everton's Marouane Fellaini retrospectively with violent conduct following his side's game at Stoke City on Saturday 15 December, 2012. The charge is in relation to an incident in the 59th minute involving Fellaini and Stoke City's Ryan Shawcross, which was not seen by the match officials, but caught on video.
"The referee confirmed that he saw two further incidents in the 71st and 91st minutes, also involving Fellaini and Shawcross, neither of which he deemed to be violent conduct."
A report on Everton's website confirmed that the Merseyside club would accept the charge.