Striker Mario Balotelli also quit training early with what reports said was a knee or thigh problem which needed examining.
Centre back Barzagli suffered his injury in Friday's woeful 3-0 friendly defeat by Russia.
"We could change a player 24 hours before the Euros. But we will try to get him fit," Italy team doctor Enrico Castellacci told Italian media a day before the squad jet off to their Euro base in Krakow.
"We are confident he can recover but in any case he would not be available in the first phase."
Inter Milan defender Andrea Ranocchia, who was in the provisional squad, could be called up if Italy decide not to risk Juventus's Barzagli.
Italy's loss to Russia, where slapstick defending was to blame for two of the goals, had led coach Cesare Prandelli to ponder switching to three at the back but Barzagli's problem changes the dynamic.
Prandelli has already had to do without left back Domenico Criscito after he was dropped when he was formally warned by police that he was under investigation for match-fixing.
The wide-ranging scandal, the second big match-fixing affair in Italy in six years, has cast a shadow over the Azzurri's preparations for their Group C opener against holders Spain on Sunday in Gdansk.