Kean sustained a muscle strain in his right thigh during training on Wednesday, the federation said, adding that he had returned to his club for recovery.
The 25-year-old enjoyed the best season of his career in 2024-25 with Fiorentina, a club he joined last summer from Juventus, scoring 19 goals to finish second in the Serie A goal scorers' standings.
Italy coach Luciano Spalletti will also be without a pair of defenders, Alessandro Buongiorno missing the Norway match through injury while Francesco Acerbi, who was in the Inter Milan side that lost the Champions League final, declined a call-up.
Italy, who failed to qualify for the last two World Cups, face a tricky start against Erling Haaland's Norway on Friday before hosting Moldova three days later in Reggio Emilia.
Norway lead Group I after winning their two opening matches against Israel and Moldova in March.