The Italian Football Federation (FIGC) announced on their official website on Thursday that Inter forward Osvaldo has suffered an adductor injury.
It is not yet known how long the 28-year-old will be out of action, but reports suggest he could be sidelined for up to a month.
Paris Saint-Germain midfielder Motta is also unavailable to coach Antonio Conte for the matches against Azerbaijan on Thursday and Malta next Monday as he is suffering with tendinitis.
The FIGC confirmed that both players will now to return to their clubs for treatment.
The news is a further blow to Conte, who already lost Milan midfielder Giacomo Bonaventura to a thigh injury, while Empoli defender Daniele Rugani earned his first call-up to the national team but later returned to Italy's Under-21 squad to cover for the injured Alessio Romagnoli.
Italy are looking to build on a 2-0 win over Denmark in their Group H qualifying opener last month.
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