Microsoft posted word of the game's delisting as part of its weekly Forza community update post:
On October 20, the original Forza Horizon for Xbox 360 will reach "End of Life" status. That means that the game and its associated DLC will no longer be available for purchase. Players who own Forza Horizon before that date will still be able to download and play the game and its associated content as normal. After that date, however, Forza Horizon and its associated DLC will no longer be for sale.
The first Forza Horizon game was first released in 2012 from developers Playground Games and Turn 10 Studios. The game was recently made available to play on the Xbox One as well via its backwards compatibility feature. The second game in the series, Forza Horizon 2, was released in 2014 for both Xbox One and Xbox 360. Microsoft's latest game in the series, Forza Horizon 3 has just been released for the Xbox One and Windows 10 for people who bought the Ultimate version, and will be released for everyone else on September 27.