According to the rate law, the rate of a reaction is given by $\text{Rate} = k[A]^n$, where $k$ is the rate constant, $[A]$ is the concentration of the reactant, and $n$ is the order of the reaction. For a zero-order reaction, $n = 0$. Therefore, $\text{Rate} = k[A]^0 = k(1) = k$. Thus, when the rate of the reaction is equal to the rate constant, the order of the reaction is zero.