Do Ultra or Master Balls exist in Pokémon GO?

You will get ultra balls as your trainer level increases. Specifically, ultra balls start showing up at pokestops once you hit level 20.

Master balls exist in the game's code, but have not been seen in game yet. Most likely Niantic will unveil them as they add features and levels in the future.

At level 12 a player unlocks Great Balls and at level 20 a player will unlock Ultra Balls. At the point of unlocking them a player will also be able to receive them from Poke Stops.

The Master Ball was indeed found in the code but it is not available to the public (yet).

A list of all level up rewards can be found here.