Hand grip strength has been considered as a possible marker for metabolic and psychiatric disease. To date, however, no research has focused on the association between alexithymia and hand grip strength. The objective of the present study was to investigate the correct association between hand grip strength and alexithymia. A cross-sectional study was carried out in Comalcalco, Tabasco, México. A total of 246 individuals were included. Hand grip strength was evaluated in the dominant hand using a Takei® portable digital dynamometer. Alexithymia was measured using the Toronto Alexithymia Scale (TAS-20). Two linear regression models adjusted by confounders were used to determine the association between alexithymia and hand grip strength. The rate for positive alexithymia was 39.0% (n = 94). Individuals with alexithymia showed a weaker hand grip strength than the comparison group (t = 2.4, 244 df, p = 0.01). Individuals with alexithymia had significantly reduced levels of hand grip strength (β = −0.39 ± 0.14; p = 0.006); after additional adjustment for clinical variables, decreased hand grip strength remained (β = 8.00 ± 1.86; p ≤ 0.001). Our results suggest that a decrease in hand grip strength could be associated with alexithymia. This measurement could be useful as a predictive marker for the identification of alexithymia in Mexican individuals who attend outpatient clinics.