A bstract The ratio of production cross-sections of ψ (2 S ) over J/ψ mesons as a function of charged-particle multiplicity in proton-proton collisions at a centre-of-mass energy $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 13 TeV is measured with a data sample collected by the LHCb detector, corresponding to an integrated luminosity of 658 pb − 1 . The ratio is measured for both prompt and non-prompt ψ (2 S ) and J/ψ mesons. When there is an overlap between the rapidity ranges over which multiplicity and charmonia production are measured, a multiplicity-dependent modification of the ratio is observed for prompt mesons. No significant multiplicity dependence is found when the ranges do not overlap. For non-prompt production, the ψ (2 S )-to- J/ψ production ratio is roughly independent of multiplicity, irrespective of the rapidity range over which the multiplicity is measured. The results are compared to predictions of the co-mover model and agree well except in the low multiplicity region. The ratio of production cross-sections of ψ (2 S ) over J/ψ mesons are cross-checked with other measurements in di-lepton channels and found to be compatible.