Barrett, 29, was shown a second yellow card for dangerous play at a ruck in Friday's loss to Rugby World Cup holders the Springboks.
He had earlier been sin-binned in his side's last match before the tournament, which they open against hosts France on September 8th.
"The independent Judicial Committee found that sending off was a sufficient sanction in this case because the player was sent off for two yellow cards," World Rugby said.
"The first of those yellow cards was for a technical offence following a team warning," it added.
The Crusaders' Barrett also avoided following the fate of England captain Owen Farrell and their number eight Billy Vunipola in missing matches for their side at next month's World Cup.
Tonga centre Georga Maoala will be unavailable until his country's final pool game after being banned for a dangerous tackle.