An independent disciplinary committee in Japan ruled Hodge's tackle on Peceli Yato should have warranted a red card for "an act of foul play," though the Australian escaped on-field punishment at the time.
Yato had earlier scored the opening try of the Pool D clash but later had to be substituted after failing a Head Injury Assessment (HIA) following the tackle.
At the time, match referee Ben O'Keeffe and video referee (TMO) Rowan Kitt ruled the tackle was legal.
Hodge's ban comes a day after World Rugby, the sport's governing body, openly criticized the standard of refereeing so far at the tournament, saying: "The match officials team recognize that performances over the opening weekend of Rugby World Cup 2019 were not consistently of the standards set by World Rugby and themselves. "
The committee concluded that Hodge's tackle constituted foul play – though reckless, rather than deliberate – as there was contact with Yato's head and a high degree of danger.
The minimum ban for such an incident is six games but the committee "acknowledged Hodge's exemplary disciplinary record, good character and conduct at the hearing," meaning his ban was reduced to three games.
Hodge will now miss Australia's remaining Pool D matches against Wales, Uruguay and Georgia but will be available for selection should the Wallabies reach the quarterfinals.
The 25-year-old has 48 hours to appeal the decision.