Chiellini, the most experienced defender in Italy’s squad with 53 caps, was forced off during the second half of Monday’s 2-0 win over Republic of Ireland, which secured a last-eight place.
“The scan he underwent confirmed it’s a strain,” said the Italy team doctor. “He will certainly miss the game on Sunday.
“Obviously, in a competition like this you have to try everything to have him back as quickly as possible but we will not take any unnecessary risks with his muscles.”
Castellacci said: “It’s nothing related to the injury he suffered just ahead of the finals.
“It’s a pity because he had recovered so well from that one but he is very motivated and has already started rehab. Let’s see what happens.”
Chiellini was replaced by Juve team-mate Leonardo Bonucci against Ireland and Bonucci is expected to now start against England on Sunday.