Barzagli suffered the injury during Friday's 3-0 friendly defeat to Russia and tests have revealed a strain to his left calf.
The Juventus defender could need up to 20 days to recover and the Azzurri have not ruled out the possibility of replacing the 31-year-old before the tournament begins this weekend.
But Barzagli retains hopes of recovering in time to play.
"Let us hope it all works out," Barzagli told Gazzetta dello Sport.
"I don't know how long I will be out for, the doctors will know that.
"The problem occurred in the last few minutes of the game against Russia on Friday when I stretched for the ball.
"At the time it didn't seem like a big issue, but I was limping the day after.
"The calf is a big muscle and if the medical staff are optimistic about my recovery then I am even more optimistic than they are.
"I feel better now, but we'll have to wait and see."
Barzagli will undergo further tests on Friday before Italy coach Cesare Prandelli decides whether to replace the experienced centre-back.
Manchester City forward Mario Balotelli did not train with the Azzurri in Tuesday morning's session as a precautionary measure after the player sustained a minor muscle problem on Monday.
Italy, who travel to Krakow on Tuesday afternoon, take on defending champions Spain in their Group C opener on June 10.
They will also play Croatia and the Republic of Ireland in the group stages.