UPDATE: Niantic Labs officially announced the existence of Ditto in Pokémon Go via the game's official Facebook page on Wednesday morning:
Professor Willow has finally discovered Ditto! Trainers all over the world have been reporting its appearance.
Ditto has been known to disguise itself as other Pokémon, so keep an eye out, some Pokémon may actually be Ditto, and when you capture them, there’s a chance that Ditto will reveal itself. If you do encounter a Pokémon that is Ditto in disguise, the Pokémon in that specific encounter will also reveal itself as Ditto for other Trainers.
Ditto is also a unique Pokémon when you interact with Gyms. When training or battling at a Gym, Ditto will copy the appearance, types, and moves of the first Pokémon it sees, and it will stay that way through the remainder of those Gym battles.
The Pokémon GO team
The company also posted its own video of what it looks like when you catch a Pokémon that's actually a Ditto: