The prisoner must pay zakaah on his wealth

If a person is kept away from his wealth, such as if he is a captive or imprisoned, then he must pay zakaah because he is the owner of the wealth. 

Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (4/275): If the owner is taken captive, zakaah is not waived in his case, whether he is kept away from his wealth or not, because his disposal of his wealth is still valid and he may sell it, give it away or appoint someone to handle it on his behalf. 

Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo’ (5/316): If the owner of the wealth is taken captive, and is kept away from his livestock, there is a difference of scholarly opinion concerning the matter. The more correct view is that zakaah must be paid, because his disposal of his wealth is still valid. Our companions said: Whether he is being held captive by kuffaar or Muslims. End quote. 

Al-Bahooti (may Allaah have mercy on him) said in Kashshaaf al-Qinaa’ (2/176): If the owner of the wealth is taken captive or imprisoned, and is prevented from disposing of his wealth, zakaah is not waived because he is still the owner. 

And Allaah knows best.