We study production of self-interacting dark matter (DM) during an early matter-dominated phase. As a benchmark scenario, we consider a model where the DM consists of singlet scalar particles coupled to the visible Standard Model (SM) sector via the Higgs portal. We consider scenarios where the initial DM abundance is set by either the usual thermal freeze-out or an alternative freeze-in mechanism, where DM was never in thermal equilibrium with the SM sector. For the first time, we take the effect of self-interactions within the hidden sector into account in determining the DM abundance, reminiscent to the Strongly Interacting Massive Particle (SIMP) scenario. In all cases, the number density of DM may change considerably compared to the standard radiation-dominated case, having important observational and experimental ramifications.