The paper presents a search for supersymmetric particles produced in proton-proton collisions at s = 13 TeV and decaying into final states with missing transverse momentum and jets originating from charm quarks. The data were taken with the ATLAS detector at the Large Hadron Collider at CERN from 2015 to 2018 and correspond to an integrated luminosity of 139 fb−1. No significant excess of events over the expected Standard Model background expectation is observed in optimized signal regions, and limits are set on the production cross-sections of the supersymmetric particles. Pair production of charm squarks or top squarks, each decaying into a charm quark and the lightest supersymmetric particle χ~10, is excluded at 95% confidence level for squarks with masses up to 900 GeV for scenarios where the mass of χ~10 is below 50 GeV. Additionally, the production of leptoquarks with masses up to 900 GeV is excluded for the scenario where up-type leptoquarks decay into a charm quark and a neutrino. Model-independent limits on cross-sections and event yields for processes beyond the Standard Model are also reported.