Misinformation about the COVID-19 pandemic proliferated widely on social media platforms during the course of the health crisis. Experts have speculated that consuming misinformation online can potentially worsen the mental health of individuals, by causing heightened anxiety, stress, and even suicidal ideation. The present study aims to quantify the causal relationship between sharing misinformation, a strong indicator of consuming misinformation, and experiencing exacerbated anxiety. We conduct a large-scale observational study spanning over 80 million Twitter posts made by 76,985 Twitter users during an 18.5 month period. The results from this study demonstrate that users who shared COVID-19 misinformation experienced approximately two times additional increase in anxiety when compared to similar users who did not share misinformation. Socio-demographic analysis reveals that women, racial minorities, and individuals with lower levels of education in the United States experienced a disproportionately higher increase in anxiety when compared to the other users. These findings shed light on the mental health costs of consuming online misinformation. The work bears practical implications for social media platforms in curbing the adverse psychological impacts of misinformation, while also upholding the ethos of an online public sphere.