It will continue to run online
On May 31st, life as we know it (on the GameSpy network) will cease to exist. It will shut down a number of games, one of which was apparently Mortal Kombat, which ran on GameSpy's infrastructure.
But Kombat lead Ed Boon has taken to Twitter to let fans know that the game will not be completely shutting down, and will still be playable in some fashion. Instead, Boon and his team will find a way to transition the game elsewhere.
Ed Boon [Twitter]