Faced with the ongoing diversification and commercial success of highly immersive media technologies (e.g., VR headsets), both content producers and scientific scholars have become highly invested in understanding the psychological consequences of experiencing media in these new and lifelike ways. While many studies underscore positive effects of high media immersivity—such as increased enjoyment or persuasive success—others warn about the intense cognitive load that technologies such as VR might put on their users. In a laboratory experiment with N = 121 participants, we compare the cognitive load experienced while watching a 360° video on a laptop screen or via an immersive VR head-mounted display. Furthermore, we scrutinize two prominent explanations for the additional cognitive load in immersive media settings, i.e., the role of spatial presence and cybersickness. As expected, the VR condition results in higher cognitive load, spatial presence, and cybersickness than the 2D condition. However, by means of a parallel mediation model, we observe that only cybersickness emerges as a meaningful mediator of participants’ strained cognitive capacity; spatial presence, on the other hand, remains statistically irrelevant in this regard. We discuss our findings considering implications for media producers and future research.