Objectives: The main purpose of this study was to examine (1) gender differences in remote teaching readiness and mental health problems among university faculty, and (2) to what extent remote teaching readiness is associated with mental health problems among university faculty, during the COVID-19 pandemic. Method: Survey participants of the study comprised 779 university faculty (58.2% men, 39.4% women, and 2.4% other gender identities or did not report) from 122 higher education institutions in the United States. Results: Chi-square tests and independent t-test findings showed that female faculty reported significantly greater remote teaching challenges -- in terms of both technology and course design -- and higher levels of anxiety and depression during the COVID-19 pandemic. Structural equation modelling results indicated that remote teaching readiness was associated with mental health problems among faculty during the COVID-19 pandemic. Conclusions: The findings suggest that gender differences in remote teaching readiness can partially explain the gender disparities in mental health problems among faculty, with female faculty being disadvantaged.