The 27-year-old England striker was sent home from the club's pre-season tour just 16 hours after landing in Thailand due to a grade one hamstring tear and will now have treatment at United's training ground as he prepares for the upcoming campain.
Moyes has revealed that Rooney first felt his hamstring in training before leaving for Asia and, following tests upon landing, it was decided not to take any risks.
But when asked whether he would be ready for the new season, Moyes told MUTV: "Yeah, he'll be okay.
"We finished training and we just thought it looked as if he just tightened up a little bit.
"He was happy with it but when we came out we thought we better just take no chances and just double check it.
"He didn't train yesterday so we thought it would be worth seeing what it was and it was just a very very slight mark on his hamstring.
"We won't take any chances, there is no point in us risking him so we've sent him back and he'll get treatment."
He added: "It's disappointing.
"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."
Rooney revealed yesterday he was 'gutted' to be leaving the tour but shared his manager's opinion that the injury is unlikely to keep him out of the start of the new season.
"Gutted to have picked up a niggling injury especially as training was going so well, heading back to Manchester to have it assessed fully but early indications are nothing to worry about," he said on his Facebook page as he headed for the airport.
The hamstring problem means Rooney will miss the trips to Australia, Japan and Hong Kong, in addition to United's tour opener against Singha All Stars in Bangkok on Saturday.
If Rooney is only ruled out for a month it would mean he could feature in the Community Shield against Wigan at Wembley on August 11.
However, given his obvious lack of match practice, it is difficult to see how he could be involved in the following week's clash between England and Scotland, or start the Premier League opener at Swansea on August 17.