A search for supersymmetric partners of top quarks decaying as t~1→cχ~01 and supersymmetric partners of charm quarks decaying as c~1→cχ~01 , where χ~01 is the lightest neutralino, is presented. The search uses 36.1 fb−1 pp collision data at a centre-of-mass energy of 13 TeV collected by the ATLAS experiment at the Large Hadron Collider and is performed in final states with jets identified as containing charm hadrons. Assuming a 100% branching ratio to cχ~01 , top and charm squarks with masses up to 850 GeV are excluded at 95% confidence level for a massless lightest neutralino. For mt~1,c~1−mχ~01 < 100 GeV, top and charm squark masses up to 500 GeV are excluded.