The Italy international suffered the injury during Juve’s 2-1 Champions League last-16 first-leg triumph over Borussia Dortmund on Tuesday.
Pirlo underwent tests on Thursday which confirmed muscle damage.
A statement from Juventus read: “Andrea Pirlo has undergone tests this morning which have revealed a first degree lesion of his calf muscle in his right leg.
“The estimated time of complete recovery is 20 days.”
Pirlo will sit out three Serie A games, including Monday’s top-of-the table clash against Roma at the Stadio Olimpico.
The 35-year-old will also miss next week’s Coppa italia semi-final first leg against Fiorentina.
The good news for Juve coach Massimiliano Allegri is that Pirlo is expected to recover in time for his team’s Champions League return leg at Borussia Dortmund on March 18.
Former AC Milan star Pirlo has scored three goals and provided three assists in 15 league appearances for the Serie A leaders this season.