Radcliffe, 29, admitted he is aware there are Internet memes of him as his most famous character Harry Potter, but he insisted, "I don't seek them out."
He then agreed to look at some of the memes Fallon had prepared.
"Yeah, please, I feel like I should be educated," Radcliffe said.
One photo showed a dog wearing Harry's signature glasses, tie and robe. It was captioned, "Hairy Pugger."
Another meme included a picture of him with the message: "If you're havin' Quidditch problems, I feel bad for you son. I got 99 problems but a snitch ain't one," a nod to the sport played in the Wizarding World.
One photo of him with his mouth wide open said: "Ron, hold on! Are those shoes on sale?"
Radcliffe can now be seen on Broadway in the comedy The Lifespan of a Fact, opposite Bobby Cannavale and Cherry Jones.