Inclusive J/ψ yields and average transverse momenta in p-Pb collisions at a center-of-mass energy per nucleon pair sNN = 8.16 TeV are measured as a function of the charged-particle pseudorapidity density with ALICE. The J/ψ mesons are reconstructed at forward (2.03 < y_cms< 3.53) and backward (−4.46 < y_cms< −2.96) center-of-mass rapidity in their dimuon decay channel while the charged-particle pseudorapidity density is measured around midrapidity. The J/ψ yields at forward and backward rapidity normalized to their respective average values increase with the normalized charged-particle pseudorapidity density, the former showing a weaker increase than the latter. The normalized average transverse momenta at forward and backward rapidity manifest a steady increase from low to high charged-particle pseudorapidity density with a saturation beyond the average value. [Figure not available: see fulltext.]