The short answer
No, in the majority opinion, but a strong exemption exists for the poor of the People of the Scripture, Jews and Christians (and adherents of religions to whom Muslim scholars have extended this status by analogy). (see What Is Zakat?)
The Zakat-ineligible categories
Six categories of people cannot receive Zakat:
The work- and earning-capable
Devotees (those who claim preoccupation with spiritual practices) who refuse to work
Inveterate unbelievers and renouncers of Islam
Children, parents, and the wives of men who are Zakat payers (see Can Zakat Be Given to Family?)
(There is also discussion about Zakat’s prohibition for the Prophet, on him be peace, and his family and descendants.)
Three groups of exceptions among the Zakat-ineligible categories
The rich (1), those who can work and earn (2), a Zakat-obliged man’s immediate relatives (6) and those who work at Zakat collection and distribution may receive payment for their services from Zakat.
The rich (1), those who can work and earn (2), non-Muslims with the status of People of the Book (Jews, Christians, and people of other religions deemed analogous) (5), and a Zakat-obliged man’s immediate relatives (6) may qualify for Zakat under the fourth class of the Zakat-eligible: those whose hearts are to be reconciled. This is the ruling of prominent groups of scholars, with the qualification that this Zakat payment eligibility cannot be determined by individual Zakat payers, but only by Muslim government authorities.
Any Muslim who is debt-ridden (Zakat-eligible category 6) can qualify for Zakat.
The detailed answer
While the majority opinion is that Zakat cannot be given to non-Muslims, there is a well-argued and supported minority opinion based on the Hanafi ruling, upheld by other eminent scholars, that Zakat Al-Fitr can be given to the People of the Book (Jews and Christians, and those analogous to them). Based on this, eminent scholars, both classical and contemporary, hold that Zakat may be paid to the poor of the People of the Book, provided that (a) the prior right of the Muslim poor and needy to the Zakat wealth paid by the Muslim rich alone is not impaired or curtailed in any way by this; and (b) that the poor of the People of the Book to whom this excess Zakat is paid do no harm to Muslims or to the religion of Islam. (see Why Muslims Pay Zakat)
Some scholars hold that the very word “needy” (miskîn) in the Quran refers not to Muslims but to the People of the Book, though this is not the position of most scholars.
Islam urges charity to all
It should be emphasized that Zakat is collected from the wealth of Muslims alone primarily for the purposes of paying it to its rightful owners, the Muslim poor, and those designated in the Quran by Allah. Yet Allah, the Quran, the Prophet Muhammad, on him be peace, and all Muslim scholars strongly exhort Muslims to give sadaqah, in the form of voluntary humanitarian charity, to all people regardless of belief. (see What Is the Difference Between Zakat and Ṣadaqah?)
Muslims have always shown humanitarian concern for others. Umar ibn ‘Abd Al-Azîz, the famed “Fifth Caliph” of Islam, wrote specifically to the governor of Basra to “look after the People of the Scripture,” especially the “elderly, infirm, and unemployed.” To each, he dispensed a sufficient stipend. Moreover, numerous verses of the Quran and instructions of the Prophet, on him be peace, urge Muslims to help all the poor and needy.
At Zakat Foundation of America, we serve people of every faith, creed, and color, providing them humanitarian aid. We deliver material help swiftly and with dignity to the direly needful of our world – the poor, the destitute, the hungry, the thirsty, the stricken, the war-ravaged, the bereaved, and the dislocated.