As far as I know marriages between jews and non jews are prohibited in Israel. Even Israel citizens have to go to Cyprus to marry.
How did this law come into existence? Is there an enforceable international law that regulates such laws?
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I have to challenge the question's frame in this answer. To say that such marriages are prohibited implies that they are forbidden. But there is nothing in Israel's law that forbids them.
Israel does not have any legal framework for state officials to officiate marriages. It does, however, recognize as legitimate all marriages performed by all clergy and all marriages (including civil marriages) performed abroad.
There is no prohibition, or any criminal or civil penalty, for Israeli citizens, Jewish or not, who marry each other in any ceremony not approved by clergy.
This does provide a practical impediment to interfaith marriages. But it also provides a practical impediment to marriages of people of same faiths who do not wish to participate in any religious ceremonies. While this point may seem tangential, it's not in Israel because a large portion of the Israeli Jews are staunchly non-religious.
However, this practical impediment is not a prohibition because, at the risk of repeating myself, it's not a legal impediment.
Israel has decided that this is the law in Israel and they are the only one who gets a say in this.
The concept of the modern nation-state can trace its origins to the Treaty of Westphalia (possibly - there is disagreement among historians and political scientists but for our purposes we'll just let them get on with it) which ended the 30-years war. This was a complex and dynamic conflict of which one of the contentious issues was who had the right to determine the laws in a particular territory, particularly religious laws - the local prince/king/duke etc. or the Emporer. Long story short - it wasn't the Emporer.
This is embodied in Article 2(1) of the UN charter:
The Organization is based on the principle of the sovereign equality of all its Members.
That is, Israel and only Israel gets to decide what the law is in Israel. Which is to say, that what the law is in Israel is down to internal Israeli politics. Israel is a democracy so this is down to democratic politics.
International law only allows involvement when the actions of a sovereign state (UN member or otherwise) infringe on the peace and stability of other sovereign states. I realise that there is a whole area of discussion here but suffice it to say that the internal operations of the UN are political rather than legal. However, laws on marriage in Israel seem unlikely to have international peace and security implications.
There are two "international law" courts, the ICC and ICJ. The ICC is generally for crimes, for example, it is currently investigating for Israel for "war crimes" against Palestine. The ICJ makes more sense here, as it can deal with individuals whose rights are supposedly being violated by states. But member states need to first accept jurisdiction. Israel hasn't committed to in every case, so they could just decline the case. But it wouldn't even go anywhere in the first place.
One could imagine the perspective of what a rights violation is expanding. Maybe in a few centuries. Or, more likely, due to demographic changes, the Western perspective of strong personal rights will be relegated to the pages of history and it will never happen.
The law originated under the Ottoman Empire from a general principle of Islamic law regarding dhimmi, non-Muslims in a Muslim state subject to that state's legal protection. Where Shari`ah governs certain aspects of life (marriage, inheritance, contract) for Muslims, each religious community can have their own system of laws. The practice dates back to the the Middle Ages, and aspects of it are centuries old in the Ottoman Empire. Put simply, Christian marriage law was that Christians marry Christians, Jewish law was that Jews marry Jews, and so on. There simply was no provision for mixed marriages. This law was not changed after the demise of the Ottoman Empire, when Britain had the mandate to run Palestine, and Israel likewise has not changed this law. It is encoded in Art. 51-56 of The Palestine Order in Council, which gives jurisdiction to the various religious courts over their respective religious communities. The law for Jews was rewritten in 1953 by the Knesset, but basically still says that marriage and divorce of Jews shall be performed in accordance with Jewish religious law, and under Jewish law (in the Talmud), there is no marriage between a Jew and a non-Jew. However, in principle a marriage between a Muslim man and a Christian woman in Israel should be possible because it is not forbidden in Islam, nor in Christianity.