The American crowd cheered as the 38-year-old tentatively posed for a picture with the scaly intruder.
Their cheers were replaced by screams and gasps however when an attempt to capture the reptile caused it to jump off the scoreboard and scurry across the court.
Officials eventually managed to throw a towel over the animal and carry it from the court, but not before it clambered up on the second scoreboard on the opposite baseline.
"Maybe the iguana got the note that this is most likely the last time I'm playing here, and he wanted to say 'Hi' and take a peek or something," Haas joked.
"It was pretty cool. Of that size, I don't think I've ever experienced that. I don't know where he came from and why he wanted to come out on Court 1 and kind of say hello to everyone."
Vesely eventually won the match when play resumed, beating Haas in three sets.