Malaria is an infectious disease caused by the Plasmodium parasite and it is transmitted among humans through bites of adult female Anopheles mosquitoes. To investigate the effects of spatial heterogeneities and seasonality, we develop a periodic reaction-diffusion model. Since the total density of mosquitoes tends to be a positive periodic solution, we are focus on the limiting system associated with the original system. We first introduce the basic reproduction number $\mathcal {R}_0$ and then show that $\mathcal {R}_0$ serves as a threshold parameter in determining the global dynamics of the limiting system by employing the theory of monotone and subhomogeneous systems. More precisely, the disease-free periodic solution is globally asymptotically stable if $\mathcal {R}_0\leq 1$, and the model admits a unique positive periodic solution that is globally asymptotically stable when $\mathcal {R}_0>1$. Finally, the threshold type result for the limiting system is lifted to the original system with the help of the theory of chain transitive sets.