The 32-year-old sat out Wednesday's session and tests on his injured back show a small herniated disc as well as a sciatic problem, reports BBC Sport.
Italy team doctor Enrico Castellacci said the recovery would "not be brief".
Buffon was replaced by substitute Federico Marchetti at half-time in Monday's 1-1 draw against Paraguay.
"A good goalkeeper is just as valuable as a striker who scores a lot of goals," stated Chiellini.
"It's obvious how much he's worth to the team."
"During the warm-up Buffon felt a pain in his back and after the first half he couldn't continue," commented Italy coach Marcelo Lippi.
"It was a big blow. We lost a substitution that we could have used.”