Moyes was also reticent on the subject of whether United will make a third bid for Barcelona midfielder Cesc Fabregas but says the Premier League champions will be welcoming a new arrival at some point.
Rooney has been subject of a pair of bids from Chelsea but United have turned them both down and insist they are determined to keep him at the club.
The England striker was at United's training ground on Tuesday amid reports he is close to handing in a transfer request.
He was there to receive treatment on the injury which ruled him out of the Stockholm friendly and Moyes said: "He's got a shoulder injury. I don't think it will keep him out very long.
"He has an injury from when he fell on it the other day in a game."
Moyes doubts Rooney will be fit for Rio Ferdinand's testimonial against Sevilla on Friday and also the Community Shield against Wigan Athletic on Sunday.
He continued: "Wayne's not going to be fit for Friday. I don't think he'll be fit and available. I hope he will be but I have a feeling he won't make it.
"As for the Community Shield on Sunday, the problem we've got is he's not played any games. He's not had any football yet and we need to take that into consideration."
Asked about Rooney's reaction to the Red Devils turning down Chelsea's latest bid, Moyes said: "I don't know. I've not asked him."
Pushed on whether he would have to convince the 27-year-old to remain at Old Trafford, the United boss replied: "You don't need to convince anyone to play for Manchester United."
As for a possible third Fabregas bid, Moyes added: "I can't say anything about it."
But, asked if reinforcements would be arriving, Moyes said: "They will."