Fellaini was charged with violent conduct by the Football Association for head-butting Shawcross during the second half of Saturday's 1-1 Premier League draw at the Britannia Stadium.
An FA statement confirmed no action will be taken over two further clashes, when Fellaini twice raised his hands in frustration at being held by his marker as the pair awaited corners.
Referee Mark Halsey saw both incidents at the time and decided neither was worthy of punishment.
Fellaini will start his suspension with immediate effect, ruling him out of the forthcoming games against West Ham, Wigan and Chelsea.
The Belgian, who apologised immediately after Saturday's game, is also likely to be fined by his club after manager David Moyes publicly condemned his player in a post-match interview.
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