We assume it was unintentional, since very few people deliberately break their legs. I have only heard of people trying to saw their legs off.
There is usually context as well, which must be provided for every question. He broke his leg playing football yesterday.
1) He broke his leg jumping off a high wall
2) He got his leg broken in a car accident
In case 1, it was due to something that he was doing. In case 2, "in a car accident" simply specifies the circumstances. So while it would be wrong in case 1 to say "intentionally", he certainly broke his leg. In case 2 hedidn't break it, it just happened to him (assuming he wasn't the driver and the accident wasn't his fault). And in case 2 I would say "got his leg broken", not "he broke his leg".
If you take "broken" as an adjective, this doesn't refer to the event, but to the current state.
If you take "broken" as a verb, it sounds like the passive version of "He or Someone else broke his leg." and we still have the question of accidentally or on purpose.
Myridon is correct. "To break one's leg" does NOT imply that one did so intentionally, and the passive voice is considered to be less of a good writing style.
If the writer/speaker WANTS to imply that someone intentionally broke his/her leg, then he would need to include details to explain that: "He broke his leg so that he wouldn't have to go to school for a month," but that would be highly unusual! Otherwise it would be assumed to be an accident (even in the case of carelessness).
Einstein's (#4) distinction is a good one: "He broke his leg" usually doesn't mean it was intentional, but it does imply that the break was due to something he did.
You normally wouldn't say "He broke his leg in an auto accident."