Not so much, anymore.
Total fertility rate by country:
Iran - 1.9
Egypt - 2.8
Algeria - 2.8.
Bahrain - 2.1
Bangladesh - 2.2
Saudi - 2.6
Turkey - 2.0
Tunitia - 2.3
Some Muslims countries are still considerably higher, but even most of those are trending down, often quite sharply.
There is a huge bulge of young people in Muslim countries, but it's temporary. There just simply is no population explosion anymore in the Muslim world.
This is very similar to the demographic change in western societies, just some decades later.
US TFR, BTW, is 1.9.
There are some real surprises in the TFR numbers. Lots of Americans think of Mexico as very prolific. Actual TFR: 2.2, not far ahead of the US.
http://data.worldbank.org/indicator/SP.DYN.TFRT.IN
No, now they are exploding in the West. And having lots of children, too. The latter raises their welfare take and increases their population share. Win-win for them.