Damon's wife Luciana gave birth to their youngest daughter Gia last month.
The couple are also parents to 2-year-old Isabella, while Damon is step-father to Luciana's 10-year-old daughter, Alexia.
"I've kind of been texting him back and forth, and he's doing great and Lucy is doing great," Affleck told People magazine at the convention last week.
Asked how his longtime friend feels about being the only male in his household, Affleck told People: "Anybody who has a child is excited, I think, no matter what the gender is. They are thrilled. The thing that people really want, when you get down to it, is a healthy child."
Friends since they were kids in Cambridge, Mass., Affleck and Damon have appeared together in the films "School Ties," "Good Will Hunting," "Dogma" and "Jay and Silent Bob Strike Back."