Measurements of the inclusive J/ψ yield as a function of charged-particle pseudorapidity density dN_ch/dη in pp collisions at s=13 TeV with ALICE at the LHC are reported. The J/ψ meson yield is measured at midrapidity (|y|<0.9) in the dielectron channel, for events selected based on the charged-particle multiplicity at midrapidity (|η|<1) and at forward rapidity (−3.7<η<−1.7 and 2.8<η<5.1); both observables are normalized to their corresponding averages in minimum bias events. The increase of the normalized J/ψ yield with normalized dN_ch/dη is significantly stronger than linear and dependent on the transverse momentum. The data are compared to theoretical predictions, which describe the observed trends well, albeit not always quantitatively.