"Following a scan this evening on a hamstring injury sustained in training, it has been decided that Wayne Rooney should return home immediately for further assessment and rehabilitation," United said.
"It is anticipated he will be unavailable for selection for a month," added the statement as Rooney prepared to fly back to England from Bangkok for treatment.
Rooney will be doubtful for the Community Shield clash with FA Cup winners Wigan Athletic at Wembley in the traditional season curtain raiser on Aug. 11 before United begin the defence of their Premier League title away to Swansea City a week later.
He has been the subject of transfer speculation since retired United manager Alex Ferguson revealed at the end of last season the England forward had asked for a transfer.
However, new United coach Moyes reiterated on Wednesday that Rooney was not for sale and would not be leaving the club.
"I have met Wayne two, three, four times. A lot has been said about myself and Wayne over the years but we have a really good relationship," said the Scot, who was manager of Everton when Rooney began his career on Merseyside.
"He is training great. They are telling me it is the best shape they have seen him in for a long time... I am going to try and get the best Wayne Rooney I possibly can," he added.
United open their tour against a Singha All-Star X1 in Bangkok on Saturday and will also play in Sydney, Yokohama, Osaka and Hong Kong before facing AIK in Stockholm on August 6.