There is absolutely no attestation of the event by anyone outside of Mathew.

However it wouldn't have been out of character. Herod had no problem killing anyone who posed even a theoretical threat to his rule. He killed his own relatives, priests, generals, and more throughout his reign. He even had his oldest son (Antipater) killed just five days before his own death. And he had no problem killing large numbers of people. He also had no problem killing on the basis of prophecy. When a group of pharisees started circulating a prophecy that his younger brother Pheoras was going to inherit the throne, Herod had those pharisees executed.

Also Bethlehem was a small town at the time. William Albright has estimated that it had 300 residents or fewer at the time. It wouldn't have had more than a dozen or so male children under 2 years old. And sadly killing a dozen toddlers wouldn't have made a top ten list of Herod's atrocities. So if it happened, it is quite possible that either Josephus didn't hear about it, because it was a small atrocity in a small town, or he thought it was not worth mentioning. I'm not sure the second part is likely though; Josephus certainly had no qualms about cataloging Herod other murderous acts.

So could it have happened? Yes. It is a plausible story. Herod was quite capable of killing kids because he heard a prophecy that one of them would take over his kingdom.

Did it happen? We don't know. We don't know who the author of the Book of Matthew was. We don't know what his sources were. And we have no corroboration.

Mugsy13 has the gist of it.

The Slaughter of the Innocents, which is found only in Matthew and contradicted by Luke's birth narrative, is a theological and literary story rather than a historical one. It closely mirrors the nativity of Moses as described in Exodus and especially in Josephus (which includes additional apocryphal detail), even directly quoting LXX Exodus at one point. The point is to set Jesus up as a second Moses.

On the historical side, there is no attestation of any such event (as QuickSpore notes), and it is considered unlikely that Jesus was born in Bethlehem. In fact, the town might not even have been inhabited at the time. Furthermore, the events surrounding and leading up to the massacre are all historically improbable (including the star and the improbable behaviour of various characters in the story). The definitive work on the subject is probably The Birth of the Messiah by Raymond E. Brown.