South African Oosthuizen, who lies second in the International points standings, does not expect to return to action until the European Tour's Sep. 26-29 Alfred Dunhill Links Championship in Scotland.
"I spoke to him about four or five days ago, and he's not going to play until the Dunhill, which is the week before the Presidents Cup," Price told reporters at Firestone Country Club on Tuesday ahead of this week's WGC-Bridgestone Invitational.
"So we really won't know if he's match-fit or not until the week before, and being one of the top four or five players that I have on the team, it's a concern.
"But I said to him, 'just get healthy first.' That's the most important thing. I don't really want him to injure himself further."
Oosthuizen withdrew from the British Open at Muirfield halfway through his opening round earlier this month with a recurrence of a neck-related injury.
It was the third time this year he had been forced out of a tournament with the injury, having also quit the Byron Nelson Championship in May and the U.S. Open in June.
"He has a hip flexor problem, and anything in the torso in the golf swing, as many of you know, can be very painful," said Zimbawbean Price, a three-times major winner.
"But we'll cross that bridge when we get to it. He's going to keep me posted on his progress, and he's gone back to South Africa to rest up."
Oosthuizen, who won his only major title at the 2010 British Open, will be missing an array of big events packed into the latter part of the PGA Tour, notably this week's Bridgestone Invitational and the August 8-11 PGA Championship.
The Presidents Cup is a biennial competition which pits a 12-man team from the United States against a line-up of international players from outside Europe.
It will be staged this year for a 10th time, with Muirfield Village Golf Club in Dublin, Ohio the host venue for a first time.
(Editing by Greg Stutchbury)
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