The Munster fly-half was cited for kicking out at Sean Cox during the 26-17 win over Edinburgh in last weekend's Heineken Cup clash.
It was feared that O'Gara could be hit with a four-week ban for the offence, but the European Rugby Cup disciplinary panel decided the player had acted "out of character".
"The Judicial Officer upheld the complaint and found that O'Gara had committed a petulant act which was out of character.
"He determined that the act was in the lower end of the IRB's sanctioning regime and taking into account the player's guilty plea and his good disciplinary record.
"Judge Blackett then determined that a two-week suspension would be wholly disproportionate to the level of offending as O'Gara had been body-checked by Sean Cox prior to the incident.
"He also accepted that O'Gara had intended to trip rather than to kick Cox. As there were no aggravating factors, he imposed a suspension of one week."
O'Gara will now sit out Munster's crucial Heineken Cup encounter against Pool 1 rivals Racing Metro at Thomond Park on Sunday.
Munster go into the game three points ahead of the French outfit, while Saracens are already assured of qualifying from the group.
And O'Gara will now be eligible for Ireland's Six Nations opener against Wales on 2 February.
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