Pirlo had announced before the World Cup this summer that he would quit playing for the national team after the tournament. However, the Juventus midfielder reversed his decision when Antonio Conte took charge of the Azzurri, telling his former club coach he would be available for selection.
The 35-year-old Pirlo returned to action on Sunday after more than a month out with a hip injury.
Bonaventura reported to the Italy camp with a right thigh injury and the Milan midfielder withdrew from the squad after tests early Monday afternoon.
Italy hosts Azerbaijan in Palermo on Friday, before making a short trip to visit Malta three days later.