Final answer:
The pineal gland is responsible for the production of melatonin, which regulates the sleep-wake cycle and circadian rhythms in the brain.
Step-by-step explanation:
The part of the brain that regulates the production of the hormone melatonin is called the pineal gland. The pineal gland is an endocrine structure located in the diencephalon of the brain, just inferior and posterior to the thalamus. Pinealocytes within the pineal gland secrete melatonin in response to low light levels, which can induce drowsiness and regulate circadian rhythms. Contrastingly, the hypothalamus regulates various bodily functions, including body temperature and circadian rhythms, but does not directly produce melatonin.