A transcript of a very informative lecture by Matthias Kuentzel. A short synopsis can't do the lecture justice, but the basic point is that while there was always anti-Jewish sentiment in the Muslim world, it also was based on the notion of Jews as an inferior group that Mohammed had defeated militarily. Anti-Semitic visions of powerful Jews being behind the world's problesm, and plotting to control the world, found most prominently in the Hamas charter, entered the Muslim world via the Muslim Brotherhood, who in turn took those ideas from the Nazis, which spent significant effort and money propagating them in the Middle East. This all started well before the creation of the State of Israel, belying the notion that the Israel-Palestinian conflict caused modern Muslim anti-Semitism. Thanks to Scholars for Peace in the Middle East for the pointer.
UPDATE: Commenters are missing the point. Islamists hate the Spanish for ruling Spain, hate the Christian minority in Arab countries, hate the Hindus who (re)conquered India from the Muslims, hate the Bahais, the Druze, and, if they're Sunni, Shiites, and so forth. And Jews were always second-class citizens in Muslim countries, though precise treatment varied from era to era, and from country to country. But there is nothing in Islam or Islamic history to explain the virulent, Protocols-style "the Jews are out to dominate the world" style of anti-Semitism that is currently prevalent in the Islamic world, unless you go to Western influences, primarily Naziism (though Soviet propaganda, not mentioned by Kuentzel, didn't help).
Nor can this be explained as a mere outgrowth of Arab nationalism regarding Zionism. Arabs aren't too fond of other ethnic groups with which they have or have had territorial conflicts, including Kurds, Africans, Persians, Europeans, and so forth. But you don't see the kind of nonsense you find in the Hamas charter directed at such groups.
One thing that I don't think Kuentzel says directly, but I think logically follows from his lecture, is that the Muslim Brotherhood not only picked up certain anti-Semitic ideas from the Nazis, but its leaders also learned from the Nazis the effectiveness of using anti-Semitism as a political tool to rally the masses and promote their form of nationalism.
That's not to say that the Arab-Israeli conflict doesn't foment anti-Semitism in the Arab world. But to acknowledge that doesn't detract from a complementary point, which is that the Arab-Israeli conflict would be less severe but for the widespread notion in the Arab/Muslim world that that conflict isn't about "Palestine," per se, but about resistance from Arabs and Muslims to a Jewish-Zionist plot to take over the entire Middle East, and ultimately dominate the world.