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.”
Chiellinin, 27, had been a doubt for the tournament after suffering a similar injury in Juve’s Serie A win against Atalanta last month.
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.