I have heard of this before aswell.
i found this info while having a google...

The theory is that the moon's gravitational pull effects the amniotic fluid in much the same way as it effects the water in the sea, rivers and even the water that's otherwise found in our bodies.
As a woman's body prepares for natural childbirth, the amniotic sac becomes distended so the point where it will easily burst if put under pressure. Under normal circumstances, the pressure of labor contractions bursts the sac. During a full moon, the pressure caused by the moon's effect on the water inside the sac can cause the same things to happen, but without the accompanying contractions