"Wayne has been sent away on a sort of hot weather break. His groin has not recovered yet," Moyes told reporters at a news conference on Friday.
"We've sent a fitness coach with him and he is away with his family. So we've given him a bit of a break. I always hoped I would be able to do that at some point in the season, but his groin is not as good as we hoped at this point."
Seventh-placed United, who were knocked out of the FA Cup at home by Swansea last weekend, hope to have Rooney back for the clash with Chelsea a week on Sunday, although Van Persie is further away from being fit.
"Hopefully we'll get him fit for the Chelsea game and we'll see how he is then," Moyes said.
"Robin is going to be a little while. We'll do everything we can to get him back quickly."
United have looked blunt without Rooney and Van Persie and Moyes goals need to start arriving from other areas.
"We've played pretty well, we just need to be a bit more clinical in the final third," he said.
"We've not been scoring enough recently."
(Reporting by Sam Holden; editing by Martyn Herman)
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