There is no official information about how new Ditto are born. Looking at this from the perspective of the video games, Ditto is not the only Pokémon that cannot be hatched from an egg. Most legendary Pokémon, including Mewtwo, Mew, and Shaymin, are unable to breed and cannot be hatched from eggs. There is a noticeable exception: Manaphy, which can breed with a Ditto. The resulting offspring is a Phione, however, which does not evolve into Manaphy. Ditto can also breed with genderless Pokémon such as Metagross.
Now, if we look at the anime, there are some discrepancies in this information. Unfortunately, there still isn't any information on how Ditto reproduces, but if we look at examples of Latios, Latias, and Lugia in the anime, it appears that these legendary Pokémon can reproduce somehow. In the fifth movie, for instance, it is mentioned that the Soul Dew is the soul of an ancestor of Latios and Latias. A baby Lugia named Silver also appeared in the anime alongside its parent.
Concerning Ditto, nothing can be concluded from this discrepancy without conjecture. If I were to draw a conjecture, it would be that the game mechanics are not directly related to the lore, and two Dittos may be able to breed. Although Senshin's theory that Ditto breed by binary fission also makes some sense.
In case you are interested in theories, you can read about the one that Ditto is a failed Mew clone. In this case, it could be that Dittos are made in a lab and don't need to reproduce.