Answer
In this counseling answer:
Only Allah (swt) knows best why people suffer from a mental illness or any other hardships. When facing hardships, the most important thing to do as Muslims is strengthening our relationship with Allah (swt). When a person is suffering from depression, it is not advisable to blame the person for their weak iman. Rather, it is better to clarify the problem and understand the level of motivation the person is experiencing to change and then give the advice within context.
As-Salaamu ’Alaikum wa Rahmatullahi wa Barakatuh,
I will do my best to answer according to my own experience and knowledge of what scholars say regarding this as well as what Islamically-centered therapists advise with some help from the team scholars, in sha’ Allah!
You wanted to ask what the Islamic cure for depression is.
There are many forms of treatment that come under Islamic Approach. For example, there are the direct suggestions, advice, and guidance from the Prophet Muhammad (saw) himself regarding managing depression by recitations of du’aa’s, etc. There are also the indirect models of Islamically-centred therapy of scholars where the emphasis of the treatment is from the Quran and the Sunnah and links are made which may be more specific to the individual who is suffering. The two models, of course, overlap but there do seem to be two distinct sets of options available.
So, as I understand, the direct options include fasting where there is a specific manner in which to fast and specifications for the food required to break the fast. This is important since diet can be a problematic issue for depression sufferers.
In addition to a renewed focus on the every day five prayers, we suggest recitation of specific du’aa’s and dhikr. Scholars suggest that there are numerous du’aa’s one may simply recite throughout the day if suffering from depression as well as offering nawafil (voluntary) prayers and reciting the Qur’an with a more detailed understanding. All of these options tend to focus on these acts alone and do not mention general practicalities of coping and living with depression.
Additionally, both approaches tend to reinforce the significance of completing the basic pillars of Islam as well as strengthening the pillars of faith to help the sufferer deal with the depressive experience in the wider context of their lives.
Often it is considered that depression is a weakness in our faith. However, it is often the case that we suffer from human frailties, as we are told in Qur’an; we are weak and we do have limits and need the support of other people or regular support over a period of time. Hence, the Islamically centered therapists tend to offer their work not as a one off but in the form of a more therapy –based sessions model. They may see a clinical necessity for following people up after their advice and consider the effect of depression on the motivation of sufferers. Of course, the model depends on the person and what they require but as I understand them, both are acceptable.
As for the second part of your question: Can depression be a result of sins? This is a tough one to answer because Allah (swt) knows best why we suffer. It depends on the person who is suffering! The scholars can best tell us if depression specifically comes to us a result of our sins but from my understanding, they have made no such mention of this in what I have read.
To this end, perhaps the best way to think about this is in the wider context of considering why we have to face difficulties at all. The answers are clearly in the Quran. I recently received an email from an excellent Sisters Circle in West London, which summarizes this beautifully as follows:
We are given problems to:
Direct us and our decisions in life towards what is best for our dunya and Akhira
Inspect us and see what our iman is made of since we may profess to be good Muslims but the proof is in the action behind our promises, not just the words!
Correct us when we have done something wrong. This, in turn, again should re-direct us to the right path, bi idh nillah! (This could be considered as the punishment.)
Protect us from something we did not know would happen or could not foresee but that Allah (swt) the Knower of the Unseen did have knowledge of.
Perfect us and our faith and increase its strength and so our place in the Akhira. 
The Correct Us interpretation in the 3d point suggests that one possible reason for illness is to teach us a lesson and return us to the Right Path. But rather than being unhappy about this, it is better that we see it as a second chance. Imagine if we made mistakes and we did not take any lessons from our behavior. We may ask why not simply be forgiven – but that is a basic behavioral principle in life; it is our lessons which change us for the better and when our mistakes are forgiven, we are more likely to repeat them because there was no lesson involved.
„A true believer does not get depressed; what does this mean?” – you asked.
I am not sure what this means in a practical sense since as I have mentioned in the above, we are sent many problems for all manner of reasons as outlined above. But from what I understand what it means is that when one’s faith is so high we are not affected by emotional problems. Therefore, the Islamic treatment for depression focuses on strengthening our faith.
Of course, the reality is that we are not all at this level of faith, and it is often said that it is when our faith is weak we suffer from such things. Allah (swt) alone knows who has the best of faith and what has led that person to it.
As a note of caution, I think it is important to be aware that when a person is suffering from depression it is not the best response to immediately blame the person for their weak iman. Rather, it is better to clarify the problem and understand the level of motivation the person is experiencing to change and then give the advice within context.
Since iman goes up and down for all of us it could quite possibly be us next time who are suffering. This sort of response often sets a person back rather than help them overcome their problem. So, we need to start with encouragement and being positive for the sake of the sufferer.
Much of the answer to these questions depends not only on the person who is suffering but also the reason for asking since so often we see different solutions for different people and their circumstances.
The above are some general guidelines, but if you require more specific information, then please do not hesitate to get in touch.
And Allah (swt) knows best.
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Disclaimer: The conceptualization and recommendations stated in this response are very general and purely based on the limited information provided in the question. In no event shall AboutIslam, its counselors or employees be held liable for any damages that may arise from your decision in the use of our services.