The 21-year-old left the Italian team's national training centre at Coverciano, outside Florence, to return to his club Fiorentina for treatment on a recurring muscle problem in his left leg.
Chiesa has scored 12 goals for Fiorentina in Serie A and the Coppa Italia this season, and is regarded as one of the rising stars of the side Roberto Mancini is building in the wake of Italy's World Cup failure.
Roma defender Alessandro Florenzi, 28, is also in doubt to face Finland after pulling up in training with a calf problem.
Florenzi's "condition will be evaluated in the next few hours," the FIGC said.
Italy's Euro 2020 qualifying campaign kicks off on Saturday with a Group J game against Finland in Udine, followed by the visit of Liechtenstein in Parma on Tuesday.