Probably you'd need a POD sometime in the late 19th/early 20th century. The early Islamist thinkers were diehard anti-Marxists, with economic policy being a crucial point here. Sayyid Qutb saw Marxism as worse than American capitalism and argued that Marxist materialism reduced mankind to animals. I guess Marx' writings on religion and "oriental barbarism" wouldn't help here either.
The only attempt at such an ideological fusion were probably Iranian writers/activists Ali Shariati and Jalal Al-e Ahmad, who combined anti-imperialism, socialism and Islamic religion as an alternative to what they called gharbzadegi (meaning something like "Westoxification"). Their ideological followers (the Mojahedin-e-Khalq) supported the Islamic revolution in 1979, but were soon wiped out under Chomeini. Shariati and Ahmad were technically not Islamic fundamentalists as we see them today, though, but rather something like an Islamic version of the liberation theologists in Latin America. Bear in mind here that in Muslim majority countries, the Marxist Left always was the mortal enemy of the Islamists, leading to partial alliances of Arab nationalists with Islamists in order to wipe out leftists (that's what happened in Baathist Iraq and Syria, as well as in Egypt under Sadat).