Zakah is taken from rich Muslims to be distributed among the poor Muslims. In principle, non-Muslims are not to be given any zakah funds but they can be given sadaqah (optional charity). An exception to this ruling is when it is a matter of life and death. In this specific case zakah can be given to non-Muslims. A portion of zakah can also be given to non-Muslims whose hearts are inclined towards Islam.

In his response to the question, Dr. Monzer Kahf, a prominent economist and counselor states:

The principle is that zakah is to be paid by rich Muslims to poor Muslims. This is according to the Hadith whose meaning I quoted; it refers to the community of Muslims.
Zakah should be paid to Muslims, not to non-Muslims except in one case: when a non-Muslim needs immediate help in a matter of life and death. On another ground, we live today in a world in which Muslims are in extreme poverty and dire need, to the extent that if all our zakah is paid to help famine-stricken Muslims it will not be sufficient to relieve them, while most non-Muslims have access to many other sources for help.

Moreover, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, adds:

The recipients of zakah, unlike ordinary charity in Islam, are primarily Muslims; Almighty Allah has specified the categories of those who are entitled to receive zakah in the Qur’an:

[The alms are only for the poor and the needy, and those who collect them, and those whose hearts are to be reconciled, and to free the captives and the debtors, and for the cause of Allah, and (for) the wayfarer; a duty imposed by Allah. Allah is Knower, Wise.] (At-Tawbah 9: 60)

however, a portion of zakah can be given to those whose hearts are inclined towards Islam; these are the non-Muslims who are on the verge of converting to Islam. Nevertheless, it cannot be given to others. Ordinary charity, however, can be given to both Muslims and non-Muslims. Islam also teaches Muslims to feed the poor in general, without any discrimination between Muslims and non-Muslims. Furthermore, Islam is emphatic about establishing good neighborliness, whether the neighbors are Muslims or non-Muslims. The Prophet (peace and blessings be upon him) said, “Jibreel continued to advise me on being good to my neighbors so that I feared that he would (one day) make him my legal heir!).” Therefore, even if zakah is only limited to Muslims, Islam never closes the doors of charity to non-Muslims.
May Allah inspire us to be charitable to all His creatures— Ameen.