In combat sports, strikes or counter-strikes response time (RT) can be related to performance and sporting success. Moreover, training sessions are usually highly fatiguing, which is expected to impair basic skills, such as RT. Thus, this study aimed to investigate the effect of fatigue on punch and kick RTs of karate practitioners. Twelve individuals of both sexes from different levels (three yellow belts, three red belts, two orange belts, two green belts, one brown belt, and one black belt) were selected. Participants were aged 22 ± 3 years old, with a stature of 169.1 ± 6.5 cm, and a body mass of 65.5 ± 10 kg. Six visits were held with each participant. On the first 2 days, the RT of punches and kicks was measured by a validated smartphone app (TReaction). For the subsequent visits, a randomized incremental test for the upper or lower body was adopted as motor fatigue protocol, immediately followed by punches and kicks RT tests, also in random order. For induction of lower and upper body-specific muscle fatigue, the ITStriker app was used, which operates by emitting sound signals transmitted by a smartphone. One-way repeated measures ANOVA was performed, and significance was set at p ≤ 0.05. Regarding the mean punches RT, significant effects between situations for the upper (F(2,22) = 11.5; ω2 = 0.23; p < 0.001) and lower body (F(2,22) = 14.2; ω2 = 0.18; p < 0.001) fatigue protocols were found. The negative effect of the lower body fatigue protocol in punches RT was evident regardless of the order of the tests (punch RT first: Δ = 10.5%; t = 4.4; p < 0.001; d = 1.0; kick RT first: Δ = 11.4%; t = 4.8; p < 0.001; d = 1.1). Regarding mean kicks RT, significant effects were found between situations for the lower (F(2,22) = 16.6; ω2 = 0.27; p < 0.001) but not for the upper (F(2,22) = 2.3; ω2 = 0.02; p = 0.12) body fatigue protocols. Kick RTs were negatively affected by the lower body fatigue protocol regardless of the RT order applied (punch RT first: Δ = 7.5%; t = 3.0; p = 0.01; d = 0.8; kick RT first: Δ = 14.3%; t = 5.7; p < 0.001; d = 1.5). Upper body fatigue does not impair punch or kick RTs. Thus, it is concluded that the specificity of fatigue protocols and striking order should be considered while performing RT demanding techniques in karate practice. Specifically, lower body motor fatigue may impair both kicks and punches RT, which highlights the role of lower limbs in punches performance. Otherwise, upper body motor fatigue seems to induce impairments that are limited to the specific motor actions of this body segment.