This study aimed to investigate the impact of Achilles tendon (AT) mechanical percussion massage (PM) on the passive stiffness of that tendon and subsequent drop jump kinematics. Eleven physically active participants performed two conditions in random order: (i) 60 s of PM applied to each AT (EXP) and (ii) no PM (CTRL). Measurements were performed 5 min before, immediately after, and 5 min following the completion of the PM. In the CTRL, measurements were performed at the same time point but no massage was applied. The two-way ANOVA indicated that there was no statistically significant interaction effect on contact time (p = 0.786), reactive strength index (p = 0.914), and relative peak power (p = 0.896). However, a statistically significant interaction on peak velocity (p = 0.046) and jump height (p = 0.03) was found. Despite that, there was no significant post-hoc comparisons for jump height, it slightly decreased 5 min post-PM (p = 0.136; ES = −0.25; Δ = −3.1%) compared with the CTRL condition (p = 1.00; ES = 0.11; Δ = +1.5%). Friedman’s test did not show significant differences in dominant (p = 0.073) and non-dominant limb (p = 0.091) AT stiffness. Although not significant, numerically, the dominant limb AT (p = 0.126; ES = −0.64; Δ = −7.8%) had a larger reduction in stiffness immediately post-PM compared with the non-dominant limb (p = 0.294; ES = −0.26; Δ = −3.6%). The results of this study indicated the temporary effect of PM on the reduction in tissue stiffness. Moreover, these findings show that a mechanical PM might slightly hinder subsequent explosive athletic performance.