The England striker had to fly back from Thailand where United have just started their pre-season tour after picking up the injury in training.
It had been reported that the 28-year-old might not be fit for United's opening Premier League game, but he wrote on his social media page that it is not as bad as first feared.
"Gutted to have picked up a niggling injury, especially as training was going so well," Rooney posted on Facebook.
"Heading back to Manchester to have it assessed fully but early indications are nothing to worry about."
Rooney has yet to confirm that he wants to stay at United, despite manager David Moyes insisting that he won't be sold.