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Whether clearly a mistake or not I'm not sure. But I do think it's still probably awkward.かぜで一週間の授業を休みました。 sounds better to me, but yours isn't really wrong. Whether to use 授業 or 勉強 depends on whether he was specifically missing classes or not.
"一週間の授業" make sense in Japanese but this phrase "授業の一週間" don't make sense.Doesn't 授業の一週間 mean "studies of one week"?