Selective recovery of indium has been widely studied to improve the resource efficiency of critical metals. However, the interaction and selective adsorption mechanism of indium/iron ions with tannin-based adsorbents is still unclear and hinders further optimization of their selective adsorption performance. In this study, the epigallocatechin gallate (EGCG) monomer, which is the key functional unit of persimmon tannin, was chosen to explore the ability and mechanism of selective separation/extraction of indium from indium–iron mixture solutions. The density functional theory calculation results indicated that the deprotonated EGCG was easier to combine with indium/iron cations than those of un-deprotonated EGCG. Moreover, the interaction of the EGCG–Fe(III) complex was dominated by chelation and electrostatic interaction, while that of the EGCG–In(III) complex was controlled by electrostatic interactions and aromatic ring stacking effects. Furthermore, the calculation of binding energy verified that EGCG exhibited a stronger affinity for Fe(III) than that for In(III) and preferentially adsorbed iron ions in acidic or neutral solutions. Further experimental results were consistent with the theoretical study, which showed that the Freundlich equilibrium isotherm fit the In(III) and Fe(III) adsorption behavior very well, and the Fe(III) adsorption processes followed a pseudo-second-order model. Thermodynamics data revealed that the adsorption of In(III) and Fe(III) onto EGCG was feasible, spontaneous, and endothermic. The adsorption rate of the EGCG monomer for Fe(III) in neutral solution (1:1 mixed solution, pH = 3.0) was 45.7%, 4.3 times that of In(III) (10.7%). This study provides an in-depth understanding of the relationship between the structure of EGCG and the selective adsorption capacity at the molecular level and provides theoretical guidance for further optimization of the selective adsorption performance of structurally similar tannin-based adsorbents.