Maguire and Jones were also injured but should be back for the league clash away to Villa on Saturday.
On Ronaldo's absence, Rangnick said: "I spoke with Cristiano yesterday before training, he told me that he's had some problems for the last couple of days.
"Minor problems, but in the end, we decided that it made more sense to not take any risks in a game that could easily last 120 minutes, so we just decided to rest him.
"He had some problems with his hip, with his hip muscle. I don't think it's anything serious."