COVID-19 has created significant challenges for higher education institutions and major disruptions in teaching and learning. To explore the psychological wellbeing of domestic and international university students during the COVID-19 pandemic, an online cross-sectional survey recruited 787 university students (18+ years) currently studying at an Australian university. In total, 86.8% reported that COVID-19 had significantly impacted their studies. Overall, 34.7% of students reported a sufficient level of wellbeing, while 33.8% showed low wellbeing and 31.5% very low well-being. Wellbeing was significantly higher in postgraduate students compared with undergraduate students. Future anxiety was significantly greater among undergraduate than postgraduate students. Multivariable regression models showed female gender, low subjective social status, negative overall learning experience or reporting COVID-19 having a huge impact on study, were associated with lower wellbeing in the first few months (May–July) of the pandemic. Supporting the health, well-being, and learning experiences of all students should be of high priority now and post-pandemic. Strategies specifically targeting female students, and those with low self-reported social status are urgently needed to avoid exacerbating existing disparities.