No, there isn't a Papa John's in Iceland, and as Erick Sims pointed out - the idea that there might be is largely down to the movie "The Secret Life of Walter Mitty".
Check out the trailer and see if you can spot some of the Papa John's product placement that Erick is talking about:
To find out whether there really are any Papa John's in Iceland, I simply checked out there company's website to find out if there are any franchise opportunities in Iceland.
Not only is there no mention of Iceland in any of Papa John's web properties, but the website Papajohns.is (.is is the top-level domain for Iceland) is not currently in use, suggesting Iceland is not one of the countries that Papa John's currently operates in.
And the product placement in the movie The Secret Life of Walter Mitty has resulted in headlines like the following:
According to Papa John's website yes they do