<p>Due to the work of Shimizu (Adv Math 355(106778):1370, 2019), various nondegeneracy conditions for braided finite tensor categories are equivalent. This theory is partially extended to braided module categories here. We introduce when a braided module category is “nondegenerate” and “factorizable”, and establish that these properties are equivalent. The proof involves a new monadicity result for module categories. Lastly, we examine the Hopf case, using Kolb’s (Proc Lond Math Soc 121:1-31, 2020) notion of a quasitriangular comodule algebra to introduce “factorizable” comodule algebras. We then show that the representation category of a quasitriangular comodule algebra is nondegenerate in our sense precisely when the comodule algebra is factorizable. Several examples are provided.</p>