It's also a very physical play with a large number of onstage fights. Fight choreography is some of the most dangerous stuff to do onstage: a single mistake and someone can easily be hit by a sword that was supposed to just barely miss them. And although stage-fighting weapons are naturally blunted, they're still big heavy metal rods that can bruise or break bones if you get hit by them. (See my P.S. for a funny story about that, BTW — nobody was injured in that one, but it came close a couple times).
There are some scenes in Macbeth that can be turned into offstage fighting if the director wants to minimize risk to the actors; for example, the battle with Macdonwald (not a typo) in Act 1 Scene 2 is reported to King Duncan, but not seen onstage in most productions. (Though an ambitious director might choose to have a mass battle depicted during the transition from Scene 1 to Scene 2, then have the combatants leave when Duncan walks onstage to hear the report). But there are three scenes that explicitly call for an onstage fight:
Act 3, Scene 3: three hired killers attack Banquo and his son; Banquo is killed but the son manages to escape. This all happens onstage.
Act 5, Scene 7: Macbeth fights young Siward, and kills him.
Act 5, Scene 8: Macbeth fights Macduff, and it's a long fight. They fight once, pause to exchange some words while both are gasping for breath, then they fight again. The stage directions call for them to exit the stage still fighting, then come back onstage still fighting, just in time for the audience to see Macduff kill Macbeth.
With three swordfights that must happen onstage, the potential for accidents is a lot higher than for most of Shakespeare's plays.
On the other hand, Romeo and Juliet has a similar number of fights, as does Hamlet — yet neither of them has acquired the same reputation. So it's also possible that there's an element of self-fulfilling prophecy going on here: actors who are worried about getting hurt might not have their full attention on the fight choreography, making them more prone to make mistakes that do actually result in injury.
P.S. Now for the funny story I mentioned. If you haven't seen The Court Jester starring Danny Kaye as the protagonist and Basil Rathbone as the villain, go watch it; it's hilarious, and it deserves to be more widely-known than it is. In the final swordfight between Kaye's character and Rathbone's, the fight ranges all over the castle, and for plot reasons, Kaye's character is alternating between fighting expertly, and making wild, amateurish swings with no skill at all. Thing is, Rathbone was an expert fencer, and helped teach Kaye (who had no fencing experience) how to fight. Now, usually in a swordfight scene, they would substitute a stuntman to double for the actor when the actor's face isn't visible. But in the scenes where Kaye's face is visible and Rathbone's isn't, it's still Basil Rathbone doing the fighting — because Kaye was so inexperienced that he was likely to make mistakes, and Rathbone didn't want anyone less experienced than himself facing an inexperienced actor in a dangerous fight scene. (In fact, if you have a lot of experience with fight choreography, you can probably spot the times when Kaye came very close to actually hitting Rathbone for real, and if Rathbone had been less experienced he might very well have been injured).
