The official version, created by Vietnam-based creator Dong Nguyen, is currently only available for Apple and Android devices.
But the publisher of the Windows Phone version is given as IG Mobile.
Flappy Bird has been downloaded more than 50 million times.
Launched in May 2013, the game has surged in popularity, promoted almost entirely by social media users, and is now the number one free game in the Apple App Store and Google Play Store charts.
On Friday, Dong Nguyen Tweeted: “I would like to [say] sorry WP [Windows Phone] users for the late of WP build. I am trying hard to make it happen.”
When the BBC alerted Microsoft to the issue, a spokesman said the company was investigating.
Vietnam-based Dong Nguyen says he has been overwhelmed by the media interest in him and his game