Ian Ringrose's answer explains that it is cheaper and less-risky for an oil-rich Arab state to build oil- or natural gas-fueled power plants than nuclear power plants.
In addition to the two non-Arab muslim countries (Iran and Pakistan) mentioned in the original post, two other non-Arab countriesothers (Turkey and Bangladesh) are currently building Russian-designed nuclear power plants. The Russian deals involve borrowing money to pay high capital costs. For example, the Bangladesh deal includes borrowing eleven billion dollars with a variable interest rate that is 1.75 percentage points higher than LIBOR, and a 28-38 year repayment period.
The Koran condemns usury, as opposed to trade. Arab countries therefore avoid interest-bearing loans. This makes it very difficult for oil-poor Arab countries to finance nuclear power plants.