It's not strictly true (Iran and Turkey are prosperous for example) but there is some truth in what you suggest. This is mainly because the West hinders their progress by sponsoring corrupt dictatorships which essentially steal all the people's money and do the Wests bidding by selling the countries produce to the West for knock-down prices. Maybe the 'Arab Spring' will change this - but I doubt it.
Also, Before the last Iraq war and before the West put sanctions on Iraq (circa 1988) that country had a higher standard of living than Belgium by some measures. Similarly Libya had a standard of living higher than Portugal or Greece before this current war. Imagine how rich Saudi Arabia would be if the oil wealth wasn't horded by a dictatorship and banked in the West?
Also, there are many Christian countries that suffer the exact same problems, e.g. Kenya, South Africa (most people are very poor there) and many other African states, so Islam has nothing to do with it.