The FA announced his punishment in a statement on its website (www.thefa.com) and said he breached Rule E3 by going on to the field in an attempt to speak to the referee.
Mourinho went on the Villa Park pitch to try and speak to referee Chris Foy after Brazilian midfielder Ramires became the second Chelsea player red-carded in the match following Willian's earlier dismissal.
The Portuguese denied an improper conduct charge but he lost his case at Wednesday's personal hearing with an independent regulatory commission. The finding was announced on Thursday.
Mourinho claimed all he wanted to do was speak to the referee who refused to speak to him and sent him off from the dugout.
Ramires was shown a straight red card for a two-footed lunge
on Villa's Moroccan international Karim El Ahmadi, which provoked a touchline row.
Mourinho claimed he was trying to speak to Foy because Ramires was pushed by Villa striker Gabriel Agbonlahor, who had been substituted.
Afterwards Mourinho said Foy should not be allowed to take charge of any more Chelsea matches and continued his complaints for days afterwards saying he "would never accept" Foy's performance.
($1 = 0.5971 British Pounds)
(Reporting by Mike Collett, editing by Pritha Sarkar)