Barnes was sent off for violent conduct after he appeared to trip the referee.
The 23-year-old forward was found guilty of behaviour which "constituted an offence whereby the standard punishment...was clearly insufficient".
He was serving a four-game ban before the FA's additional punishment.
Barnes denied the FA charge, but a regulatory commission heard the case on Friday morning and found him guilty.
His original four-match ban had included an extra game for his second dismissal of the season.
The former Plymouth player missed the 2-1 defeat at Barnsley on Tuesday and will now only be available for Brighton's last three games of the Championship season.
Following injuries to Craig Mackail-Smith and Will Hoskins, Leonardo Ulloa is now Brighton's only recognised first-team striker.
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