All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
At the present, time many misconceptions –like the one you mentioned in the question –are widespread.
The answer to this misconception is as follows:
1- Many scholars stated that there is a consensus among the scholars that Zakah should not be given to a non-Muslim except those on whom there is a difference of opinion, i.e. those who are inclined towards Islam and it is hoped to attract their hearts. As regards giving Zakah to a non-Muslim without any restrictions, then it is agreed among the scholars that it is forbidden to give it to him, as reported by Ibn Qudaamah and others . For more benefit, please refer to Fataawa 87316 and 82875.
2- In principle, Zakah money is not added to the treasury; rather, what is practised during the first generation is that the Zakah-collector distributes the Zakah among the poor of the area from which it is collected, acting according to the advice of the Prophet to Mu’aath “It (Zakah) should be taken from the rich amongst them and be given to the poor amongst them.” Moreover, there is a difference of opinion among the scholars about the permissibility of transferring the Zakah from one country to another and many of them did not permit it. The Zakah money is not taken to the treasury unless there is no poor in the area from which it is collected who may take it. It is reported that ‘Umar criticized Mu’aath for sending Zakah money to him, and Mu’aath apologized to him that he did not find anyone to take it.
3- Claiming that Zakah is the only source of the treasury is not correct, and we already clarified to you that in principle Zakah money is distributed amongst the poor in the area from which it is collected and that it was not added to the treasury.
As regards the main sources of the treasury, they were as follows: a) the fifth of the booty, b) the spoils which the Muslims got without war, c) the money whose owners are not known –and it was much at that time because of the conquests when many non-Muslims went in exile from their countries, d) the land tax on the countries which were conquered by force such as the Levant, Iraq and Egypt, and which was imposed by ‘Umar who saw the benefit of leaving the land in the hands of its owners in exchange for the payment of a land tax, and e) the Jizyah, which was the tax imposed on the rich adult non-Muslim people who live freely in a Muslim land. Therefore, whoever claims after all this that Zakah is the only source of the treasury is absolutely wrong.
Hence, we advise you to get around the outstanding scholars who are known for their knowledge and piety, and avoid those people who raise misconceptions.
We ask Allaah to guide us and all the Muslims to the straight path.
Allaah Knows best.