Topical application of drops containing ocular drugs is the preferred non-invasive route to treat diseases that affect the anterior segment of the eye. However, the formulation of eye drops is a major challenge for pharmacists since the access of drugs to ocular tissues is restricted by several barriers. Acetazolamide (ACZ) is a carbonic anhydrase inhibitor used orally for the treatment of ocular hypertension in glaucoma. However, large ACZ doses are needed which results in systemic side effects. Recently, we synthesized copolymers based on 2-hydroxyethyl methacrylate (HEMA) and a functionalized three-arm poloxamer star (Bayfit-MA). The new material (HEMA/Bayfit-MA) was engineered to be transformed into nanoparticles without the use of surfactants, which represents a significant step forward in developing new ophthalmic drug delivery platforms. Acetazolamide-loaded nanocarriers (ACZ-NPs) were prepared via dialysis (224 ± 19 nm, −17.2 ± 0.4 mV). The in vitro release rate of ACZ was constant over 24 h (cumulative delivery of ACZ: 83.3 ± 8.4%). Following standard specifications, ACZ-NPs were not cytotoxic in vitro in cornea, conjunctiva, and macrophages. In normotensive rabbits, ACZ-NPs generated a significant intraocular pressure reduction compared to a conventional solution of ACZ (16.4% versus 9.6%) with the same dose of the hypotensive drug (20 µg). In comparison to previously reported studies, this formulation reduced intraocular pressure with a lower dose of ACZ. In summary, HEMA:Bayfit-MA nanoparticles may be a promising system for ocular topical treatments, showing an enhanced ocular bioavailability of ACZ after a single instillation on the ocular surface.