The triple Grand Slammer sustained the injury in training last week and suffered a reaction over the weekend.
He underwent scans on Monday and the Ospreys are confident it is not a serious problem but his return to action has been delayed.
The formidable scrummager had been set to make his first appearance of the new season off the bench for the Ospreys against Glasgow on Friday.
“Adam took a bump last Tuesday in training,” said Ospreys head coach Steve Tandy.
“He carried on through the session and trained Thursday and Friday.
“Then all of a sudden, over the weekend, it started to stiffen up a little bit.
“We scanned him just as a precaution and I’m waiting for the physios to take another look at the scan.
“But I don’t foresee him being out for a large period. It’s not a real major injury for him. It’s settling down a little bit.
“He’ll probably be out for a couple of weeks. He will definitely miss this weekend and potentially the Scarlets game (Sept 21).
“Then hopefully we’ll have him back available for us against Munster at the end of this month (Sept 29).
“We were looking to have him come off the bench this weekend. It would have been great to have him in, but it’s something we can’t do.”