The interactions between emotion and attention are complex due to the multifaceted nature of attention. Adding to this complexity, the COVID-19 pandemic has altered the emotional landscape, broadly heightening health and financial concerns. Can the heightened concerns about COVID-19 impair one or more of the components of attention? To explore the connection between heightened concerns about COVID-19 and attention, in a preregistered study, we collected survey responses from 234 participants assessing levels of concerns surrounding COVID-19, followed by four psychophysics tasks hypothesized to tap into different aspects of attention: visual search, working memory, sustained attention, and cognitive control. We also measured task-unrelated thoughts. Results showed that task-unrelated thoughts, but not survey reports of concern levels, negatively correlated with sustained attention and cognitive control, while visual search and working memory remained robust to task-unrelated thoughts and survey-indicated concern levels. As a whole, these findings suggest that being concerned about COVID-19 does not interfere with cognitive function unless the concerns are active in the form of task-unrelated thoughts.