The 27-year-old suffered a cut to the forehead following a clash with Phil Jones during a training session ahead of England's World Cup qualifiers against Moldova and Ukraine.
While some reports have claimed that Rooney is targeting the Manchester derby as his return on September 22, Moyes has refused to set a date.
"He is in great physical shape," Moyes said in a press conference. "Obviously he has a cut right in the middle of his forehead which could split because the skin is very thin.
"He has had his stitches out and it has knitted. We just have to see where the level of risk is with his injury."
Meanwhile, midfielder Marouane Fellaini could make his debut for United against Crystal Palace tomorrow.