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Indium is considered a candidate low-temperature solder because of its low melting temperature and excellent mechanical properties. However, the solid-state microstructure evolution of In with different substrates has rarely been studied due to the softness of In. To overcome this difficulty, cryogenic broad Ar⁺ beam ion polishing was used to produce an artifact-free Cu/In interface for observation. In this study, we accomplished phase identification and microstructure investigation at the Cu/In interface after long-term thermal aging. CuIn₂ was observed to grow at the Cu/In interface and proved to be a stable phase in the Cu–In binary system. The peritectoid temperature of the Cu₁₁In₉ + In → CuIn₂ reaction was confirmed to be between 100 and 120 °C. In addition, the growth rate of CuIn₂ was discovered to be dominated by the curvature of the reactant Cu₁₁In₉/In phase and the temperature difference with the peritectoid temperature. Finally, a comprehensive microstructural evolution mechanism of the Cu/In solid-state interfacial reaction was proposed.