We demonstrate that the scalaron, a scalar degree of freedom, emerging from the f(R) theory of gravity, can account for the observed dark matter (DM) abundance if its mass is around the MeV scale, to ensure its cosmological stability. Focusing on two well-known f(R) gravity models, we systematically show that if scalaron production proceeds via the freeze-in mechanism, the right relic abundance is satisfied over a very narrow window of reheating temperature 1014 ≲ Trh ≲ 1016 GeV. We delineate the viable parameter space of the f(R) models consistent with the observed DM abundance, and highlight relevant experimental constraints from searches targeting DM decay signatures.