Central midfielder Pirlo, who has just recuperated from a long lay-off, is suffering from acute pain.
The 29-year-old earlier tore a right thigh muscle two months ago, and was sidelined for a long while as a result.
On the other hand, up-and-coming striker Pato sustained a bruising in the Rossoneri's last Serie A match against Palermo.
Even though he hasn't been seriously injured, the Brazilian ace was substituted on the half hour mark, and now he is ruled out of the Coppa Italia match as a precaution.
Carlo Ancelotti's men want to pull their act together after slumping to a 3-1 loss to Palermo on Sunday in the Serie A.
In addition to the pair's absence, the Rossoneri's clash against the Biancocelesti won't be a walk in the park, as the latter are eager to make amends for their 2-0 defeat to Atalanta in the weekend.