The 2006 World Cup winner, injured in Thursday's 2-1 friendly defeat by Mexico, will travel to South Africa with the team on Tuesday but faces a race to be fit for the second Group F game against New Zealand on June 20.
The Italian football federation said in a statement the 31-year-old would miss the Paraguay match in Cape Town.
"It's an injury which worries me but there's time," team doctor Enrico Castellacci told reporters earlier, saying the recovery period was at least 15 days.
"The intention is to take him to South Africa to see if he can be fit. Before June 13 we can change players in the squad."
Pirlo, who would have been a definite starter, has left the Azzurri's training camp in the Italian Alps to rest at home.
He was due to miss Saturday's final friendly with Switzerland in Geneva in any case after coach Marcello Lippi said he would use players who did not feature against Mexico.
Pirlo's dead-ball ability and neat passing were key to Italy's 2006 triumph but he has struggled for AC Milan in the last two years.
