What is the medical terminology for broken penis?

It is commonly referred to as a Justin Bieber penis. Please note: Justin Bieber does not actually have a penis.
Penile fracture, penis fracture, but "broken penis" works just fine too.

Considering there is no bone in the penis, it cannot be broken. A fractured penis is when the erected penis becomes ruptured. In this case it becomes a medical emergency so treatment is paramount.