That depends on what you mean by depression.

The clinical term will be hard to map to ancient texts. There is a large social component to (most, if not all) mental illness, even today there are vast differences between the diagnoses (and even illnesses) of much of the world. Add hundreds of years onto that and the differences in how people were expected to behave become even more pronounced. Clinically diagnosing them as an individual from 2015 doesn't really make much sense, or have many applications.

That all being said, ancient theater is extremely interesting to read as a psychologist. "The Eumenides" follows Orestes after he killed his mother. He ends up pursued by the Furies, a group of deities that want him brought to justice. Throughout the play you're able to see how Orestes wrestles with his issues and 'unhappiness'. I won't use the word depression, but there are some similarities.

I'm out of time, but hopefully others will be able to chime in as well. (Especially since I more talked about the question topic than answered it).

You might find this article interesting.
http://www.theatlantic.com/health/archive/2014/01/diagnosing-mental-illness-in-ancient-greece-and-rome/282856/