Hooper pleaded guilty to a charge of foul play at a hearing on Tuesday, the Australian Rugby Union said in a statement, and a two-week ban was reduced to one because of his "early admission and good behavioural record".
Hooper, Australia's vice captain, will subsequently miss the meeting with the Welsh on Saturday but will be available for the quarter-finals the following week.
Saturday's match at Twickenham will decide which of the countries tops the pool, with the losers likely to face twice world champions South Africa in the quarter-finals.
Hooper's absence will be a blow to the Wallabies, who have used him and his fellow openside flanker David Pocock to great effect in victories over New Zealand, Fiji and England this season.
Australia have a wealth of options in the back row, however, and openside Sean McMahon and the versatile Ben McCalman both scored two tries and were the best players on the pitch when the Wallabies fielded a second string side against Uruguay.
"We have got a squad of 31 and that's the reason you have a squad of 31," attack coach Stephen Larkham said on Tuesday.
"We have a couple of excellent players waiting for their chance -- Ben McCalman and Sean McMahon have both played really well in the tournament.
"McMahon, McCalman have put their hands up in this tournament. We may have to chop and change. Sean could slot in at seven, or Ben can go to eight and Pocock at seven."
Fullback Israel Folau could also miss the match after turning his ankle in the victory over England last weekend, Larkham said.
The former rugby league international, an almost permanent starter since making his debut against the British and Irish Lions in 2013, was taken off in the 65th minute of the Twickenham triumph last Saturday.
Larkham said winger Rob Horne, who injured his shoulder in the match, would almost certainly miss the match against Wales but Folau was also a worry.
"The other injury concern is Izzy," he added. "He came off the field in the game with a sore ankle and didn't train yesterday, so we'll see how he pulls up today and whether he trains."
Kurtley Beale is most likely to fill in at fullback against the Welsh if Folau is unable to start.
(Reporting by Nick Mulvenney, editing by Sudipto Ganguly)
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