The South American duo missed PSG's mid-season training camp in Morocco and were reported to have returned late to their first session back on French soil.
Both Cavani and Lavezzi have been linked with moves away from the French capital club, who visit Montpellier in the Coupe de France on Monday.
And PSG have been quick to sanction the pair, forcing them to train separately from the rest of the squad and sit out the cup clash at the Stade de la Mosson and Saturday's Ligue 1 trip to Bastia.
"Lavezzi and Cavani will train away from the group until Saturday and will not participate in the next two games," Blanc said.
"It is unacceptable. When one puts his personal project above the collective I can become a bit radical."
However, Blanc was coy on the subject of prospective exits for Cavani and Lavezzi, while stressing his desire to keep hold of midfielder Adrien Rabiot - who is reported to be close to joining Tottenham on loan.
"There may be movement. Purchases, loans, sales, but it's a bit too early to talk about," Blanc added.
"I want to keep Rabiot. He re-signed, he is part of the future. But it is a very complicated issue."
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