Short answer
Yes, the tenant does. A security deposit held by a landlord or a deposit scheme is still the tenant's money and will come back, so it is zakatable like money owed to you. You may pay its zakat each year or when you get it back. The landlord does not count it as his wealth.
A refundable deposit remains the depositor's property, or a debt owed to him, and so is zakatable for him; its zakat may be paid each year, or for all the years when it is returned. The one holding it does not count it as his own wealth.
The four schools agree on this.
Explanation
When you rent a flat, the deposit you pay does not stop being yours. The landlord or the deposit scheme holds it, and you expect it back when you leave, less any fair deductions. In zakat terms it is money owed to you, and money owed to you that you expect to recover is zakatable.
How to count it: add the amount you expect to get back to your zakatable wealth on your zakat date. If you already know part will be kept for damage or unpaid bills, leave that part out. You may pay its zakat every year with the rest of your zakat, which is simplest, or pay for all the years together when it is returned. See zakat on money owed to you.
The same applies to other refundable deposits: utility deposits, a deposit on a leased car, or a refundable booking deposit. A non-refundable fee is spent and is not counted.
For the landlord, the tenant's deposit is not his wealth. If it sits in a protected scheme, he leaves it out. If it is mixed in his own account, he should not count it as his, since he owes it back. Rent he has collected and still holds is his, and zakatable; see zakat on rental property.
The evidence
Quran, Surah An-Nisaa 4:58
۞ إِنَّ ٱللَّهَ يَأْمُرُكُمْ أَن تُؤَدُّوا۟ ٱلْأَمَٰنَٰتِ إِلَىٰٓ أَهْلِهَا وَإِذَا حَكَمْتُم بَيْنَ ٱلنَّاسِ أَن تَحْكُمُوا۟ بِٱلْعَدْلِ ۚ إِنَّ ٱللَّهَ نِعِمَّا يَعِظُكُم بِهِۦٓ ۗ إِنَّ ٱللَّهَ كَانَ سَمِيعًۢا بَصِيرًۭا ﴿٥٨﴾
Indeed, Allah commands you to render trusts to whom they are due and when you judge between people to judge with justice. Excellent is that which Allah instructs you. Indeed, Allah is ever Hearing and Seeing.
A deposit is held in trust and belongs to the one who paid it.
Where the ruling is recorded
- al-Durr al-Mukhtar with Radd al-Muhtar, Kitab al-Zakat, on the three kinds of debt. Money owed to a person by someone who acknowledges it is zakatable for the creditor.
- al-Hidaya, Kitab al-Zakat, opening section on the conditions of zakat. Zakat is due on what a person owns; wealth held for another is not his.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.