Words that count days use an exceptional reading. Even though this is a jukugo word, it uses kun'yomi readings for both the kanji. Think about this word this way:
Ten days is just TOO (とお) long from now. Why do you have to wait until the tenth day? Maybe fewer would have been okay, but ten is too many.
Please take this medicine for ten days.
Please complete it within ten days.
The tenth of July is the anniversary of my grandfather’s death.