Abstract Angular correlations of heavy-flavour and charged particles in high-energy proton–proton collisions are sensitive to the production mechanisms of heavy quarks and to their fragmentation as well as hadronisation processes. The measurement of the azimuthal-correlation function of prompt D mesons with charged particles in proton–proton collisions at a centre-of-mass energy of $$\sqrt{s} = 13$$ s = 13  TeV with the ALICE detector is reported, considering $$\mathrm D^{0} $$ D 0 , $$\mathrm D^{+} $$ D + , and $$\mathrm D^{*+} $$ D ∗ + mesons in the transverse-momentum interval $$3< p_{\mathrm{T}} < 36$$ 3 < p T < 36  GeV/ $$c$$ c at midrapidity ( $$|y| < 0.5$$ | y | < 0.5 ), and charged particles with $$p_{\mathrm{T}} > 0.3$$ p T > 0.3  GeV/ $$c$$ c and pseudorapidity $$|\eta | < 0.8$$ | η | < 0.8 . This measurement has an improved precision and provides an extended transverse-momentum coverage compared to previous ALICE measurements at lower energies. The study is also performed as a function of the charged-particle multiplicity, showing no modifications of the correlation function with multiplicity within uncertainties. The properties and the transverse-momentum evolution of the near- and away-side correlation peaks are studied and compared with predictions from various Monte Carlo event generators. Among those considered, PYTHIA8 and POWHEG+PYTHIA8 provide the best description of the measured observables. The obtained results can provide guidance on tuning the generators.