The COVID-19 pandemic has spread throughout the world, leading to school and university closures. A practical response to minimize the negative effects of the COVID-19 pandemic depends largely on students’ voluntary adherence to government guidelines as well as their participation in volunteering activities and their willingness to take national responsibility. From the perspective of the self-determination theory (SDT) of motivation, it is postulated that for students to willingly participate in volunteering activities and take national responsibility, three basic psychological needs (BPN) of autonomy, competence, and relatedness must be fulfilled. We investigate the extent to which satisfying these needs is associated with an increase in searching for opportunities to volunteer, sense of national responsibility, and the quantity of volunteering made. A total of 215 Saudi male and female participants were involved in the study. Our analysis showed that the three needs are satisfied among the sample and that no gender differences existed. Regarding the correlation analysis, the results revealed that the three BPN were significantly correlated with the sense of national responsibility and searching for opportunities to volunteer but not with the quantity of volunteering made. The results highlighted the key role that the three BPN play in understanding Saudi students’ levels of participation in volunteering and taking on national responsibility. The results are discussed in light of the pandemic context.