"Vieri has an operation on his knee and won't be available," Lippi told Italian media.
Vieri sustained the injury in Monaco's clash with Paris St Germain in the French League late in March.
It was initially thought he would be out for one month, but Monaco said on Monday that the 33-year-old forward won't be available for the World Showpiece.
"In the light of the evolution of Vieri's injury, the player will undergo a knee surgery in the coming few days," read a statement posted on Monaco's official website.
Vieri's injury is bad news for Italy who also miss Sampdoria midfielder Aimo Diana through a groin injury.
"Diana is struggling with a persistent groin injury that won't be right in time so he won't be able to be called up," Lippi added.
Sports leading magazine Football Italia reported that Livorno's Cristiano Lucarelli and Parma's Marco Marchionni are likely to replace the injured duo.