<p>Dengue is a mosquito-borne disease that is rampant worldwide, with up to 70% of cases reported to be asymptomatic during epidemics. In this paper, a reaction-diffusion dengue model with asymptomatic carrier transmission is investigated. We aim to study the existence, nonexistence and minimum wave speed of traveling wave solutions to the model. The results show that the existence and nonexistence of traveling wave solutions are fully determined by the threshold values, which are, the basic reproduction number <i>R</i>₀ and critical wave speed <i>c</i>* &gt; 0. Specifically, when <i>R</i>₀ &gt; 1 and the wave speed <i>c</i> ≥ <i>c</i>*, the existence of the traveling wave solution is obtained by using Schauder’s fixed point theorem and Lyapunov functional. It is proven that the model has no nontrivial traveling wave solutions for <i>R</i>₀ ≤ 1 or <i>R</i>₀ &gt; 1 and 0 &lt; <i>c</i> &lt; <i>c</i>* by employing comparison principle and limit theory. As a consequence, we conclude that the critical wave speed <i>c</i>* is the minimum wave speed of the model. Finally, numerical simulations are carried out to illustrate the effects of several important parameters on the minimum wave speed.</p>