The England forward suffered a tightness of his hamstring during a training session in Thailand, and Moyes has said that there was little to achieve by keeping him on their Asian trip.
"It's disappointing [but] we won't take any chances, there is no point in us risking him so we've sent him back [home] and he'll get treatment," Moyes told MUTV. "The day we left he just felt his hamstring tighten up right at the end of training and we felt there would be no problem.
"But after the long flight we decided we'd get him tested and scanned and there is just a small grade one injury there.
"So there is no point is us taking him another halfway round the world so we've sent him back. He'll be okay [for the new Premier League season]."
Rooney's future is currently the subject of intense speculation, with the former Everton teenager being linked with moves to Paris Saint-Germain, Arsenal and Chelsea.