Meteorite showers are the remains of extraterrestrial objects which are captivated by the gravitational field of the Earth. We have analyzed the mass distribution of fragments from 16 meteorite showers for scaling. The distributions exhibit distinct scaling behavior over several orders of magnitude; the observed scaling exponents vary from shower to shower. Half of the analyzed showers show a single scaling region while the other half show multiple scaling regimes. Such an analysis can provide knowledge about the fragmentation process and about the original meteoroid. We also suggest to compare the observed scaling exponents to exponents observed in laboratory experiments and discuss the possibility that one can derive insight into the original shapes of the meteoroids.