The defender damaged knee ligaments during last night's World Cup qualifier between Argentina and Colombia.
"What a terrible thing that happened to our Nicolas Burdisso," wrote the Giallorossi captain on his blog. "He is a pillar for Roma and a guarantee, not to mention a reference point for the locker room and the defence.
"It will be a truly heavy absence. Nico, you've got grit to spare and we know that well. You are a warrior.
"Give it all you've got this time too. Roma are waiting for you."