(1) Background: Suicide is the main cause of death in Italian prisons. The largest number of inmates who killed themselves was recorded during three years of the COVID-19 pandemic. This study aimed to explore psychosocial risk factors for suicide among inmates incarcerated before and after the onset of COVID-19. (2) Methods: At prison reception, inmates underwent clinical interviews and were assessed using the Blaauw Scale and Suicide Assessment Scale. Psychological distress, measured by the Symptom Checklist-90-R, was compared between inmates admitted before and after COVID-19. Regression analyses were run to examine psychosocial vulnerabilities associated with suicidal intent in newly incarcerated individuals at risk of suicide. (3) Results: Among the 2098 newly admitted inmates (93.7% male) aged 18 to 87 years (M = 39.93; SD = 12.04), 1347 met the criteria for suicide risk, and 98 exhibited high suicidal intent. Inmates who entered prison after the onset of COVID-19 were older and had fewer social relationships. They had a higher prevalence of recidivism and substance abuse, along with elevated levels of psychological distress. An increase in perceived loss of control, anergia, obsessive-compulsive symptoms, phobic anxiety, and paranoid ideation emerged as the factors most strongly associated with high suicidal intent. (4) Conclusions: These findings support the value of psychosocial screening in promptly identifying inmates at risk of suicide, enabling the implementation of targeted, multi-professional interventions. Future research should replicate these results, with a focus on longitudinal studies that monitor the same inmates throughout their incarceration period.