The rumours started on Twitter and suggested the pop star had been in a car crash.
It was also suggested he was suffering from heart failure.
A publicist for the band said the online reports were "false" and a "total hoax".
The band's official Twitter account also tweeted: "Stories reporting that Neil has been seriously injured are a hoax. PSB HQ."
The Pet Shop Boys are set to play 10 dates in America in April as part of the Electric 2014 tour, including a headlining slot at the Coachella music festival in California.
The publicist added: "He is alive and well. Read their Twitter. He wasn't even in Germany."