The England striker, who has been sidelined for several weeks, will miss Saturday's home Premier League game against Wolverhampton Wanderers and Wednesday's derby at Manchester City.
GEAR:Save 10% on Wayne Rooney shirts here, courtesy of online retailer Kitbag
"He is going on Saturday and will return the following Saturday," Phelan told a news conference that he was attending in place of manager Sir Alex Ferguson who was ill with a virus.
"It might be in the interest of him and the club to have a change of scenery. He has had a lot of attention lately so we are going to give him the best possible opportunity that we can to be in good shape when he returns."
Rooney, who has been in the headlines for several months in the run-up to signing a five-year deal to stay at Old Trafford because of allegations about his private life and his poor form, has been struggling with an ankle injury.
Phelan said Rooney would be under the supervision of United's medical staff during his week at a training facility in Oregon, on the west coast of the United States.
"He needs the conditioning, he can go there without the attention he would get around here," said Phelan.
"If that goes according to plan, then he's available when he returns."
INJURED PLAYERS
United are without several injured players for the Wolves match, which falls on the day Ferguson celebrates 24 years at the club.
The 68-year-old manager, who has been feeling under the weather since returning from Turkey midweek with a virus that has also affected players including Anderson and Darron Gibson, would be at the game, said Phelan.
Portugal winger Nani misses out with a groin injury he picked up in Tuesday's 3-0 Champions League victory at Bursaspor, while midfielder Ryan Giggs is a major doubt having just returned to training after an injury.
Phelan said Nani was feeling better than expected after his knock and could be in contention for the Manchester derby.
There was even better news for midfielder Darren Fletcher, though, who is in contention for a place on Saturday after showing "positive signs" of recovering from his ankle injury sustained midweek.
After a shaky start to the season where on several occasions United conceded late goals to draw from winning positions, they seem to have tightened up after five consecutive victories in all competitions.
"We're starting to get a rhythm," said Phelan.
"We feel as if we might have got over these lapses of concentration and we are getting more of a settled unit now and that is proving in the performances and the results that we get."
