An Islamic Expert explained it very all on AllExperts (and it was cited from IslamToday, who cited from Saudi research group on Fatwa's and Islam). I will attempt to summarize, but I am not a Muslim therefore if there are improper summaries, it's my fault.
Why is MLM and Pyramid Scheme illegal under Shariah (Islamic law)?
1) Usury, or handing over small amount of money, and get huge rewards later, is illegal under Shariah. Pyramid scheme fits this definition.
2) Shariah prohibits "uncertainty business", or business with significant degree of chance. MLM and pyramid scheme, where you don't know if you can recruit enough people, is such an "uncertainty business".
3) Shariah prohibits taking other people's money through false promises. Pyramid scheme, where you must pay to join, is prohibited.
4) Shariah prohibits deception and outright fraud, such as misrepresenting payment as "commission", misrepresenting a fraud as a business, and so on.