We extend the soft theorems for scattering amplitudes of scalar effective field theories to one-loop order. Our analysis requires carefully accounting for the fact that the soft limit is not guaranteed to commute with evaluating IR-divergent loop integrals; new results for the soft limit of general scalar one-loop integrals are presented. The geometric soft theorem remains unmodified for any derivatively-coupled scalar effective field theory, and we conjecture that this statement holds to all orders. In contrast, the soft theorem receives nontrivial corrections in the presence of potential interactions, analogous to the case of non-Abelian gauge theories. We derive the universal leading-order correction to the scalar soft theorem arising from potential interactions at one loop. Explicit examples are provided that illustrate the general results.