O'Connor was in extreme pain on the field following the aerial collision and, after bravely attempting to play on, was taken from the field with more than a quarter of their 30-21 Super Rugby loss remaining.
Coach Damien Hill said O'Connor was having breathing difficulties on the day and the Wallabies utility was kept in hospital on Sunday for further tests.
Next week's bye will mean the Rebels don't need to rush O'Connor back and Hill will also have a significant selection dilemma to ponder over before the club's round-11 meeting with the Bulls in Melbourne.
Hill admitted he didn't know what Kurtley Beale's best position was and said he would consider shifting the former Waratah to No 10.
Flyhalf Danny Cipriani made a couple of key errors in Saturday's loss and, although Hill wasn't unhappy with the Englishman's performance, he said he would give serious thought to Beale at No 10 as he looks to turnaround their bottom-placed position in the Australian conference.
"It's a really good question - I think he made a really good impact at 10," said Hill, who moved his key attacking weapon into the front line for the final quarter of the Waratahs match.
"I think he's a dynamite 15. I think what it comes down to is the competition for spots there.
"Julian Huxley's performing well at 15 (off the bench) and Danny had a reasonable game (last night) at 10, so it's a good problem to have obviously. I think Kurtley likes both."
Waratahs counterpart Michael Foley might face a similar decision this week, with No 15 Bernard Foley's shoulder injury possibly opening an opportunity for him to try Berrick Barnes at the back.
The Waratahs don't have an accurate prognosis on Bernard Foley, but coach Michael said Barnes and Adam Ashley-Cooper would be considered for the switch if required.
Giving his thoughts on Beale's best position, the Waratahs coach said his former pupil could dominate in both positions, even at Test level.
"Fullback gives him the opportunity to come into the game
where the defence wouldn't expect it, but he played 10 a number of
times for us last year and was exceptional there so I'd be pretty
confident he could do it at the highest level there either way," Foley
said.