Barrett was sent off after being shown a second yellow card for a dangerous clean out on Springbok hooker Malcolm Marx in the first half of New Zealand's record 35-7 defeat at Twickenham.
He had only just returned to the field after being sent to the sin bin for a foul at the breakdown, when New Zealand were on a team warning for repeated infringements.
The independent Disciplinary Committee was chaired by Sir James Dingemans (England), joined by former international player Olly Kohn (Wales) and former referee Valeriu Toma (Romania).
The committee found that sending off was a sufficient sanction in this case because the player was sent off for two yellow cards (referred to as temporary suspensions in the appendix), and the first of those yellow cards was for a technical offence following a team warning.
Barrett is available for selection for the opening World Cup match between New Zealand and hosts France in Paris on Saturday, 9 September (NZT).
Meanwhile, the All Blacks have dropped two places to fourth in the world rankings following their record defeat to the Springboks.
Fiji have climbed to seventh following their win over England with the English slipping to eighth.
South Africa and France are up to second and third behind top-ranked Ireland.