In this letter, we present the first measurement of the energy-energy correlator (EEC) in charm-tagged jets from proton-proton (pp) collisions at $\sqrt{s} = 13$ TeV. EECs probe the structure of QCD radiation, providing a unique test of mass-dependent effects in parton showers involving a charm quark and offering a distinct view into non-perturbative phenomena, including the hadronization process. The EEC is measured for charm-tagged jets and flavor-untagged (inclusive) jets with transverse momenta of $10 <~ p_{\rm T} <~ 30$ GeV/$c$, where charm-quark mass effects are significant. We observe a significant suppression of the EEC amplitude in charm jets compared to inclusive ones, consistent with the expected suppression of radiation from massive quarks -- a fundamental prediction of QCD. Despite the significant amplitude difference, the observed peak positions of the charm and inclusive-jet EEC are similar, indicating a complex interplay between Casimir factor (differentiating quark and gluon jets), and quark-mass (dead-cone) effects in the QCD parton shower as well as subsequent hadronization effects. Comparisons with next-to-leading order calculations and various Monte Carlo event generators reveal the sensitivity of this observable to both mass effects in the parton shower and hadronization process. These results provide new constraints on theoretical models of heavy-quark jets and offer insights into the parton-to-hadron transition in QCD.