Arbeloa made his remarks following Fulham's 1-1 draw with United in the Premier League at Craven Cottage in September.
Matheus Cunha equalised for visitors United in the 89th minute.
Arbeloa, who admitted the charge, has also received a warning for his comments, with the FA saying the Spaniard "acted in an improper manner by making comments in a post-match interview that imply bias and/or question the integrity of a match official".
London club Fulham are currently bottom of the Premier League with just two points from their opening six games.
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