The individual giving Zakaat should be Muslim
The order for Zakaat is only for Muslims. Almighty Allah has ordered the believers to give Zakaat along with offering Salaat. Almighty Allah says in the Holy Quran:
And (always) establish Prayer and pay Zakat (the Alms-due) regularly. And whatever virtue you will send ahead, you shall find it with Allah. Surely, Allah is watching all that you are doing. Surah Baqarah (2:110)
All the Jurists (Fuqaha) agree that if a non-Muslim embraces Islam, then he/she will not be ordered to give the Zakaat of the life preceding Islam. If someone leaves Islam, may Allah protect us from that, and later on again embraces Islam, then that person will not be asked to give the Zakaat for the period that he/she was not a Muslim. As given in Al Bahr Ur Raaiq Sharh Kanz Ud Daqaaiq, Vol. 2, Pg. No. 354.