The veteran playmaker was withdrawn in the 2-1 Champions League win over Borussia Dortmund on Tuesday and has since undergone tests on the problem.
The Serie A champions have now stated that Pirlo has suffered a first-degree strain of his right calf and is likely to be sidelined for 20 days.
He is therefore expected to miss Juve's next four matches, including the top-of-the-table clash with Roma and the Coppa Italia semi-final against Fiorentina on March 5.
However, the 35-year-old should be in contention to feature in the second leg of their last-16 tie in Dortmund on March 18.
Goals from Carlos Tevez and Alvaro Morata gave Juventus their slender advantage to take to Germany, although Marco Reus's away goal means that the outcome of the tie remains in the balance.