"The scan this morning showed a noticeable improvement in the player's calf," Italy team doctor Enrico Castellacci was quoted as saying by ANSA.
"We have decided to keep him, he won't be available for the first two matches but we will try to get him fit for the third. There is silent optimism."
Defender Davide Astori had been flown in as cover in case Barzagli had to be sent home.
Italy, who face holders Spain in their Group C opener in Poland's Gdansk on Sunday, are set to use a new system with three at the back and midfielder Daniele De Rossi playing in the centre of defence, partly because of Barzagli's injury.
"You are not talking with a central defender," a smiling De Rossi told reporters. "You are talking with a player who is willing, that knows how to adapt and to accept everything.
"Maybe I could become the best defender in the world."