Lockdown, social isolation, and interruption of daily life during the COVID-19 period have impacted many lives. University students are particularly vulnerable to such disruptions and may be particularly disposed to suicidal ideation, potentially creating a new public health crisis. This study aimed to assess suicidal ideation and associated factors among university students in Bangladesh during the early stages of the COVID-19 pandemic. A cross-sectional online survey was conducted using the Google form (Google survey tool) from April to May 2020. Initially, 3366 respondents voluntarily completed the survey form. Finally, 3331 surveys were included in the final analyses after removing incomplete surveys. The data ware reviewed, rechecked, and analyzed with SPSS (25.0 version) software. A total of 1979 (59.4%) males and 1352 (40.6%) females participated. Respondents were between the ages of 18 to 28 years (mean age 21.4 years [SD = 1.9]). The prevalence estimate of suicidal ideation was 12.8%. Potential risk factors included less sleep, excess sleep, cigarette smoking, past suicidal thoughts, suicide attempt history, family history of suicidality, depression, anxiety, and stress. Potential protective factors included being male, having lower SES, living in rural areas, regular physical exercise, and satisfactory study. Suicidal ideation was prevalent among Bangladeshi university students during the onset of the COVID-19 pandemic. Understanding the correlates of suicidal ideation may aid to develop targeted strategies to support students during and after the COVID-19 pandemic.