The 34-year-old goalkeeper played in Saturday's 3-3 draw with Eintracht Frankfurt but it was confirmed on the club's official Twitter page that he will not be available on Tuesday.
Ralf Fahrmann is expected to replace Hildebrand in goal for the clash in what will be his second appearance of the season.
"Goalkeeping change in Bucharest," the club tweeted. "Schalke will be without Hildebrand with a bruised right hip.
"(He) maybe fit again on Saturday."
Hildebrand has played 12 of Schalke's 13 league fixtures this season and has been an ever-present in the Champions League.
Jens Keller's side sit in second in Group E with two games remaining with two games remaining.
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