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Dubai Airports Security & customs has the information (added emphasis mine):
Customs
Like all countries, we have rules about what you can and canβt bring with you. Everyone who arrives must pass through customs, so please check the list below beforehand. Some items can result in fines or, in cases such as narcotic drugs, imprisonment.
Personal allowances
- Gifts not exceeding AED 3,000.
- Cash above AED 100,000 must be declared.
- Maximum of 400 cigarettes, 50 cigars, 500 grams of tobacco.
- Maximum of 4 litres alcohol, 48 cans of beer.
- Medication: A maximum three-months supply of medication for your personal use. Please include an original prescription from a registered medical practitioner. All medications should be in original packaging, and not expired. No psychotropic medicines are allowed (even for personal use, in small quantity and/or with prescription) without prior approval from the Ministry of Health.
Items you cannot bring into the UAE
- All narcotic drugs.
You would want to be extremely cautious regarding medicine: