Bentancur fell awkwardly when attempting a header and teammates looked concerned as he lay motionless on the pitch.
He was taken off the field on a stretcher after lengthy treatment on the pitch and underwent observations in hospital.
"It looks like a concussion but nothing more than that. He was in the hospital, obviously, and they did all of the tests in terms of checking, making sure everything is okay," Postecoglou told reporters on Friday ahead of his team's FA Cup third-round clash at non-league side Tamworth.
"And all good. He is back home. He is fine. He is feeling good. We'll obviously follow the protocols now. I think it is a couple of weeks where you have to make sure everything is okay."
The news will be a relief to Bentancur, who served a seven-match ban this season for comments he made about teammate Son Heung-Min during a TV interview.
As well as missing the trip to Tamworth, Bentancur will have to sit out next week's Premier League trip to Arsenal and the clash against Everton but could return for the Europa League fixture against Hoffenheim on January 23rd.