Yoga has not been proven to treat the chemical imbalance that causes clinical depression, but a gentle yoga practice can introduce depressed individuals to simple physical activities, which benefits overall mood and physical health. Serious clinical depression, (as opposed to just a passing depressed mood) can lead to a decrease in an individual's physical activity, so introducing a short and easy yoga practice helps disrupt sedentary habits caused by depression.
Though yoga doesn't exactly cure depression, studies have shown that the practice can have a definite positive effect. For example, a 2013 study from Duke University showed that yoga practice was helpful for several mental illnesses, including depression.
The study revealed that yoga practice can have a beneficial effect on the brain's chemical messengers, similar to the way that antidepressant drugs act. However, in these studies the people practiced yoga mostly in groups, so it is difficult to say whether the social exposure or the yoga itself was responsible for the study participants' positive response.