The centre-back had not featured in Thursday's friendly against Estonia, a game the Azzurri won 4-0 to stretch their unbeaten run to 20 matches.
"I wanted to be there at all costs, but unfortunately I can't," Bonucci said in an interview with Rai Sport on Saturday.
"I pushed hard and gritted my teeth in the last 20 days, including against Lazio in the last half-hour when I felt discomfort.
"Unfortunately it is a crescendo of pain, I am forced to stop. In Turin, we will evaluate the recovery times."
Gagliardini, meanwhile, has left the national squad ahead of the fixture against Poland in Reggio Emilia after returning an inconclusive result in Friday's Covid-19 tests.
The Inter midfielder tested positive at the start of October, though had seemingly recovered as he was cleared to return to action for his club.
After coming off the bench in Inter's 1-1 draw with Atalanta on November 8, the 26-year-old played the entire game for Italy against Estonia.
However, with the outcome of a second swab test taken on Saturday still not known, the Italian Football Federation announced Gagliardini is to return to Milan, meaning he will not be part of the travelling party for the trip to Sarajevo either.
"During yesterday's checks ahead of Italy vs. Poland, Roberto Gagliardini’s test results were inconclusive. He already had previously tested positive for Covid-19 at the beginning of October following swab tests with his club; however, he then recovered from the virus and returned a negative result," Italy confirmed on the FIGC's official website.
"Since the test results are not always certain in their detection of Covid-19 in cured persons, a second swab was taken this morning, the outcome of which is expected in the evening.
"Taking into consideration the journey this morning to Reggio Emilia and the subsequent trip to Sarajevo on Tuesday, the player, although asymptomatic, will return to Milan as a precautionary measure."