The experienced center back has not traveled to Ukraine for Wednesday's Champions League group game, with Anderson, Fabio and Wilfried Zaha also not involved.
Both sides won their opening Group A fixtures, with the Premier League champion beating Bayer Leverkusen 4-2 and Shakhtar winning 2-0 at Real Sociedad.
United will be without its 34-year-old center back for the second fixture in the group in Donetsk, though Moyes has revealed he would not have taken part in the match even if he was fit.
"Rio has a slight groin problem," Moyes told reporters. "It is nothing serious, but I was never bringing him anyway."
The United boss, looking to bounce back from his side's surprise defeat to West Brom on Saturday, will also be without Brazilian duo Fabio and Anderson, while Wilfried Zaha has not traveled either.