tl;dr: Effectively yes, it does, but in principle mostly-no.
Land ownership, leasing, and planning-of-use are a complicated issue, especially in Israel/Palestine. I won't provide a full and detailed explanation of the various aspects of the situation, but rather try to paint a few broad strokes to support the tl;dr statement above.
In Israel, most land is officially owned by the state. This is a legacy of the land registration mechanism and social order common to the Ottoman empire, which differed from European feudalism; the Sultan owned (almost) all land, formally; and the semi-equivalents of feudal landlords were empire-mandated tax collectors. The tax collector (and his hierarchy of deputies/delegates etc.) had no claim to the land itself. And while in Europe, commons and feudal estates were eventually divided up into the private ownership common today, in Ottoman Palestine this had happened only partially by the time the British and then the Zionists took over. A land registry was only started in the 19th century (!) ; the result was, that Israel was instituted 'inheriting' the vast majority of land in the sovereign territory as formally state-owned land. ... and Israel has not, and will not, sell or give out land to (non-Jewish) Arabs. It actually doesn't typically sell land at all, and rather offers long-term leases. IIANM, most Israelis who own apartments and houses - do not own the land those are built on, but rather hold a very-long-term lease.
Israel also rarely leases out parcels of lands to (non-Jewish) Arabs either, as such lease-outs regard planned construction of new towns/settlements or expansion of existing ones; and Israel's planning policy allows almost exclusively for settlement by Jews. There are a few exceptions to this rule - IIANM there have been some expansions of already-established Arab or mixed-Arab-Hebrew localities, and Israel has created new permanent settlements into which it moved some of the semi-nomadic Bedouin population in the Naqab region. But other than that, no new Arab settlements have been created since Israel was formed, over 75 years ago.
On the other hand - Israel does not, to the best of my knowledge, restrict sale of real-estate by private owners to Arabs. So, if a person or organization owns an apartment or house, or a piece of land, they can sell it to an Arab. I believe non-Arabs selling land to Arabs is extremely rare though - it is somewhat of a taboo, as it runs counter to the purpose of the Zionist movement and the state of Israel in general, which is driving out the native Palestinian (Arab) population in favor of a state of the Jewish colonists. The idea is for Arabs to lose land, not regain it.
One of the bulwarks against Arabs getting land is the "Standing Fund for Israel", also referred to as the Jewish National Fund. This was the organizational instrument of land purchases and distribution for Jewish settlement before Israel was formed, and today still it owns a significant fraction of the total land of the Israel. Unlike formal state institutions, which are in theory partially committed to non-discrimination, the JNF is explicitly chartered to deny Arabs its land; so the state can use, and has used, the transfer of ownership or control of lands to the JNF as a means of developing Arab-free settlements, while pre-circumventing arguments regarding discrimination in land allocation and planning policies.