Fallon joked in his "Late Night" monologue Wednesday that he hasn't had a chance to respond to everyone's messages, "but let me just say - Yes, William and Kate, we'll definitely set up a play date."
Fallon and his film-producer wife, Nancy Juvonen Fallon, welcomed their daughter Tuesday morning.
The 38-year-old Fallon takes over NBC's "The Tonight Show" from Jay Leno next year after hosting "Late Night" since 2009.
Fallon thanked fans for their support on social networks and joked about chasing people down to show them pictures of his baby: "Now I understand why people are on Facebook. I get it now, I get it."