Balotelli had been called up for the first time under Antonio Conte, despite his poor form, but the Liverpool striker strained his lower back and adductor muscles.
Ogbonna has a left hamstring injury and medical staff decided not to risk the Juventus defender.
It is a blow for Conte, with fellow defender Leonardo Bonucci suspended against Croatia.
Italy plays Croatia in a key European Championship qualifier on Sunday at San Siro — where Balotelli formerly played for both Inter and AC Milan.
Italy and Croatia both top the group with nine points.
The Azzurri then travel to Genoa for a friendly match against Albania on Tuesday.
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