Chiesa missed Italy's 5-0 hammering of Lithuania on Wednesday with a muscle problem and even though tests revealed no injury Allegri said the 23-year-old would be left in Turin for Saturday's match.
"The tests were negative but as a precautionary measure I spoke to the lad and while he seems OK, when you feel like there is something wrong, even something really small, it's a risk playing in a high-intensity match like the one tomorrow night," Allegri told reporters.
As well as Chiesa, Juve will be without attackers Paulo Dybala and Juan Cuadrado, midfielder Rodrigo Bentancur and defenders Danilo and Alex Sandro as they are returning too late from their respective qualifiers.
Allegri said that Cuadrado was the only one of those players who could have made the match at the Stadio Diego Armando Maradona but will stay in Colombia after suffering an attack of gastroenteritis.