The no-arms tackle caught the Fijian flanker in the head in the 26th minute of the Pool D opener in Sapporo on Saturday but the Wallabies utility back was cleared of an offence by the matchday officials, despite the protestations of the Fijian players.
Yato was unable to return to the field after failing a head injury assessment and was also forced to miss Fiji's shock defeat by Uruguay in Kamaishi last night, in line with concussion protocols.
Hodge was subsequently cited the next day and an independent disciplinary committee ruled on Wednesday night that he should have received a red card under the high tackle sanction framework, but deemed the tackle to be reckless rather than deliberate.
The punishment was halved from six weeks because of his "exemplary disciplinary record, good character and conduct at the hearing".
Hodge who has 48 hours to appeal the decision, will miss Australia's clash with Six Nations champions Wales on Sunday as well as games against Uruguay and Georgia. He will be free to play again in the World Cup if the Wallabies advance to the knockout stage.