I have been reading up on polymorph spells, and I want to know if there is any way to gain a Medusa's Petrifying Gaze. Monsterous Physique grants special abilities based on what level of the spell you are casting, but gaze is not listed there. Does that mean you can't gain a monsterous humanoid's gaze attack at all?
Monsterous Physique Does not Grant Gaze
You are correct, the Monstrous Physique spell does not grant Petrifying Gaze. It specifically lists the abilities and bonuses that you can gain from polymorphing into those creatures.
Generally You Cannot Polymorph for a Gaze Attack
Proving a negative claim is difficult, when it's possible. All I can provide is some general guidance. In general, Pathfinder's polymorph ability has been significantly changed from D&D 3.5's. Polymorph no longer grants access to supernatural or spell-like abilities. This is on purpose.
Additionally, polymorph is segregated into different spells based on the type of creature you want to change into. Monstrous Physique is used to change into monstrous humanoids, for example. As far as I am aware, no other spell accomplishes this task. So there is likely no way polymorph can grant you the Medusa's petrifying gaze.
You can cast Flesh to Stone to generally produce the same effect. It is a level 6 spell, compared to level 3 for Monstrous Physique.