Independent judicial officer Alan Hudson, from Canada, ruled the offence was "low-end" which would normally receive a two week ban.
The punishment was downgraded because of Hooper's early admission, good conduct during the hearing, good character and the absence of any off-field aggravating factors.
Losing Hooper is a blow for Australia who are determined to top Pool A. Whichever team wins at Twickenham on Sunday morning (NZT) has an easier path through the playoffs, playing either Scotland or Japan in the quarter-finals.
The loser would likely face the Springboks in the first knockout match and then a possible semifinal against the All Blacks, should they beat either Ireland or France.
The tactic of having Hooper and Pocock, both openside flankers, on the field at the same time has paid dividends in wins over the All Blacks and England this year and would likely have been repeated against the Welsh, who also have mobile loosies.
With Hooper gone, his replacement is likely to be either Ben McCalman or Sean McMahon.
At a press conference held before the disciplinary hearing, Wallabies assistant coach Stephen Larkham admitted he was surprised Hooper was cited but the team were content with the judicial process.
"We have a couple of excellent players waiting for their chance - Ben McCalman and Sean McMahon have both played really well in the tournament.
"In saying that Michael has been tremendous so far, and in fact the games before the tournament he was the standout as well. It is hard to replace someone like that, but the guys are certainly ready to go."
Hooper himself was surprised to face the judiciary after the high of another tournament victory had subsided.
"I was a bit shocked to find out I was being cited from the weekend," said Hooper. "However I think I had a fair trial and can move on and help the team be in the best position for this weekend and train with them.
"Personally you want to play in every test match that you can. So straight away it's a huge disappointment that I can't be involved, and put myself forward for selection. And secondly to be a part of a team in a World Cup and not be there is again another blow. I'll be doing my best to help out the guys for this weekend."
Larkham said McMahon could be a direct swap for Hooper in the number seven jersey, or Pocock could shift there and be replaced at Number 8 by McCalman.
The former World Cup winning Wallaby also revealed Folau's injury problem and confirmed Horne was unlikely to play.
"[Folau] came off the field in the game [against England] with a sore ankle and didn't train yesterday, so we'll see how he pulls up today and whether he trains."
Appointed as part of Michael Cheika's coaching group after the shambolic departure of Ewen McKenzie late last year, Larkham dismissed any talk of complacency in the Wallabies camp particularly on the back of a 10 match winning streak against Wales.
The Welsh, who have injury concerns of their own, have not beaten the Wallabies since a 21-18 victory at Cardiff in 2008.
"I think it is a really big test for us. The experience they have in the second row and their forward pack as a whole is something we definitely respect, and we are going to have to prove on the field that we can match them.
"I guess the focus we have going into this game is like any other - we have to make sure our prep is right," said Larkham.
"Michael took over at the end of last year and tried to change a few things within the culture and playing style and they are coming to fruition now. Those old games against Wales have no relevance to this weekend."
- By Jared Savage in London
