Background: Mental health concerns of university students are gaining more attention since the emergence of the coronavirus disease. Consequently, scholars in education, health and psychology-related fields have attributed the dwindling subjective well-being (SWB) of students to their low levels of digital health literacy (DHL). However, little attention has been paid to an important variable like pocket money (PM) which might serve as a buffer against reduced levels of SWB. In this study, we explored the dynamics of PM and its linkage with DHL and SWB among university students in Ghana. Methods: With a cross-sectional design, a convenient sample of 1160 students was obtained from the University of Education, Winneba, Ghana. The COVID-DHL and WHO-5 Well-being instruments were used for the data collection for a 2 months period (February–March, 2021). Chi-square test, multivariate regression, simple linear regression, and PROCESS mediation analyses were performed with the use of SPSS software version 25. Results: The study found that while most of the students were financially supported by their parents (n = 715, 61.6%), a larger proportion of them reported that their PM was either less sufficient or not sufficient (n = 550; 76.9%). Findings revealed a positive relationship between PM and SWB (B = −36.419, p < 0.001; B = −13.146, p = 0.012; B = −10.930, p = 0.043), with this relationship mediated by DHL (B = −1.139, confidence interval [CI] [−2.073, −0.263] vs. −2.300, CI [−4.290, −0.532] vs. −8.366, CI [−14.863, −1.908]). Conclusions: Students with little to insufficient PM were vulnerable to mental health problems, although this could be buffered by the high DHL levels. In practical terms, not only should the PM of university students be increased, but the sources of PM should be complemented since the sufficiency level of PM was associated with the source of finance. More importantly, parents should be empowered through job creation so that sufficient levels of PM can be provided to university students.