In this paper we establish some regularizing and decay rate estimates for mild solutions of the Debye–Hückel system. We prove that if the initial data belong to the critical Lebesgue space $${L^{\frac{n}{2}}(\mathbb{R}^{n})}$$ , then the L q -norm ( $${\frac{n}{2} \leq q \leq \infty}$$ ) of the βth order spatial derivative of mild solutions are majorized by $${K_{1}(K_{2}|\beta|)^{|\beta|}t^{-\frac{|\beta|}{2}-1+\frac{n}{2q}}}$$ for some constants K 1 and K 2. These estimates particularly imply that mild solutions are analytic in the space variable, and provide decay estimates in the time variable for higher-order derivatives of mild solutions. We also prove that similar estimates also hold for mild solutions whose initial data belong to the critical homogeneous Besov space $${\dot{B}^{-2+\frac{n}{p}}_{p,\infty}(\mathbb{R}^n)}$$ ( $${\frac{n}{2} < p < n}$$ ).