(1) Background: Joint hypermobility refers to joint movement beyond normal range. Dentistry requires fine motor skills and manual dexterity; thus, the presence of hand joint hypermobility requires early assessment and intervention. The aim of this cross-sectional study was to assess the prevalence of hand joint hypermobility among first-year dental students and investigate correlations between the severity of their hypermobility and muscular strength. (2) Methods: First-year dental students were evaluated by an occupational therapy team composed of certified hand therapists. The extension of distal interphalangeal, proximal interphalangeal, and metacarpophalangeal finger joints was assessed with bilateral testing of digit hypermobility (with a cut-off of >20° for hypermobility) and classified as high, moderate, or low risk according to number/types of joints involved. Muscular strength was assessed by comparing grip strength, lateral pinch, and three-point pinch to norm values. Right- vs. left-handed individuals, and females vs. males were compared with an independent t-test; the relationships between the variables were investigated using the Pearson correlation. (3) Results: Out of 141 dental students (24.6 ± 3.0, 70% females, 87% right-handed), 15% and 16% were classified as having a high and moderate risk of hypermobility, respectively, with no sex difference. Right-handed students scored significantly higher in the right lateral pinch than left-handed students (18.2 ± 4.8 vs. 13.2 ± 4.1, p = 0.045). A higher severity of hypermobility was associated with bilateral lower grip and pinch strength (p < 0.05). (4) Conclusions: One third of the first-year dental students exhibited moderate to severe hand joint hypermobility. Moreover, those identified as having moderate to severe hand joint hypermobility showed a decreased grip strength.