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.
Defender Giorgio Chiellini will be fit to play at least a half following a knock.
BIG BLOW
Lippi already has a doubt over winger Mauro Camoranesi, who has a knee injury, and the loss of Pirlo for any games at the World Cup would be a big blow to the holders.
Castellacci said Camoranesi was progressing well.
Lippi had already put midfielder Andrea Cossu, left out of the 23-man squad, on alert to go to South Africa if Camoranesi was not fit and the Cagliari man would also be the most like-for-like replacement for Pirlo.
If both Pirlo and Camoranesi are not fit for the tournament, midfielder Antonio Candreva could come in having been in the provisional 30-man squad.
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.
Italy meet Slovakia in their final group game on June 24.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
