Background: The mechanism that could increase intraocular pressure (IOP) during scleral lens (SL) wear is not fully understood, although it may be related to compression of the landing zone on structures involved in aqueous humor drainage. Methods: Thirty healthy subjects were fitted with two SLs of different sizes (L1 = 15.8 mm, L2 = 16.8 mm) for 2 h in the right eye and left eye as a control. Central corneal thickness (CCT), parameters of iridocorneal angle (ICA), Schlemm’s canal (SC), and optic nerve head were measured before and after wearing both SLs. IOP was measured with a Perkins applanation tonometer before and after lens removal and with a transpalpebral tonometer before, during (0 h, 1 h, and 2 h), and after lens wear. Results: CCT increased after wearing L1 (8.10 ± 4.21 µm; p < 0.01) and L2 (9.17 ± 4.41 µm; p < 0.01). After L1 removal, the ICA parameters decreased significantly (p < 0.05). With L2 removal, nasal and temporal SC area and length were reduced (p < 0.05). An increased IOP with transpalpebral tonometry was observed at 2 h of wearing L1 (2.55 ± 2.04 mmHg; p < 0.01) and L2 (2.53 ± 2.22 mmHg; p < 0.01), as well as an increased IOP with Perkins applanation tonometry after wearing L1 (0.43 ± 1.07 mmHg; p = 0.02). Conclusions: In the short term, SL resulted in a slight increase in IOP in addition to small changes in ICA and SC parameters, although it did not seem to be clinically relevant in healthy subjects.