The global SARS-CoV-2 outbreak and subsequent lockdown had a significant impact on people’s daily lives, with strong implications for stress levels due to the threat of contagion and restrictions to freedom. Given the link between high stress levels and adverse physical and mental consequences, the COVID-19 pandemic is certainly a global public health issue. In the present study, we assessed the effect of the pandemic on stress levels in N = 2053 Italian adults, and characterized more vulnerable individuals on the basis of sociodemographic features and stable psychological traits. A set of 18 psycho-social variables, generalized regressions, and predictive machine learning approaches were leveraged. We identified higher levels of perceived stress in the study sample relative to Italian normative values. Higher levels of distress were found in women, participants with lower income, and participants living with others. Higher rates of emotional stability and self-control, as well as a positive coping style and internal locus of control, emerged as protective factors. Predictive learning models identified participants with high perceived stress, with a sensitivity greater than 76%. The results suggest a characterization of people who are more vulnerable to experiencing high levels of stress during the COVID-19 pandemic. This characterization may contribute to early and targeted intervention strategies.