The Italian Football Federation announced the withdrawal of both players on Sunday. Politano and Mancini were injured in the draw against North Macedonia on Saturday (1-1) and suffered a calf injury and a thigh injury respectively.
New coach Luciano Spalletti, who also had to do without striker Federico Chiesa and midfielder Lorenzo Pellegrini, both of whom were out of Saturday's draw in Skopje, called in Bologna striker Riccardo Orsolini as reinforcement.
Italy are third in Group C, three points behind second-placed Ukraine after playing a game more.
The two teams will face off on Tuesday night at the San Siro stadium in Milan.