Etzebeth went off in the first half of South Africa's 18-3 win over Scotland on Sunday and Erasmus said he would go for scans.
"We might find out it's much more serious, but at this stage it looks like a 10-day injury," South Africa director of rugby Rassie Erasmus said on Monday.
Etzebeth is the most experienced player in the South Africa squad with more than 100 Test caps, and is a pivotal figure in the forward pack.
On the time frame Erasmus talked of, the key second rower would be ready again around three days before the highly-anticipated match between the defending champion Springboks and world No.1 outfit Ireland on September 23.
But that doesn't guarantee Etzebeth will be able to play, Erasmus said, given that he may miss some training in the week before the game.
"We'll have to make the right call because we can't have players who are 70 or 80 per cent," Erasmus said.
Etzebeth did not appear to be in too much discomfort and watched the rest of the Scotland game from the bench, and even joined in on a lap of honour afterwards.
The winner of the match between the world's top two will also likely avoid playing hosts, on-form France, in the quarterfinals, although that would only mean a probable last-eight clash with three-time champions New Zealand instead.
Erasmus also said he didn't expect centre Jesse Kriel to be cited or face any disciplinary action over a tackle that led to a head clash against the Scots, and which drew scrutiny for possibly being worthy of a red card.
Erasmus said he thought that Kriel first made contact with the ball being carried by Scotland No.8, the former Wallaby Jack Dempsey, and "we're very happy with how it was refereed."
"I'm pretty sure there won't be a citing," Erasmus said.
Scotland coach Gregor Townsend saw the hit in the game's opening minutes differently and said he had expected it to be examined by television match officials.
Referee Angus Gardner, of Australia, and the TV officials took no action and allowed play to go on.
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