Short-wave infrared (SWIR) emitters are at the center of ground-breaking applications in biomedical imaging, next-generation optoelectronic devices, and optical communications. Colloidal nanocrystals based on indium arsenide are some of the most promising SWIR emitters to date. However, the lack of single-particle spectroscopic methods accessible in the SWIR has prevented advances in both nanocrystal synthesis and fundamental characterization of emitters. Here, we demonstrate an implementation of a solution photon correlation Fourier spectroscopy (s-PCFS) experiment utilizing the SWIR sensitivity and time resolution of superconducting nanowire single-photon detectors to extract single-particle emission linewidths from colloidal indium arsenide/cadmium selenide (InAs/CdSe) core/shell nanocrystals emissive from 1.2 to 1.6 μm. We show that the average single InAs/CdSe nanocrystal fluorescence linewidth is, remarkably, as narrow as 52 meV, similar to what has been observed in some of the most narrowband nanostructured emitters in the visible region. Additionally, the single nanocrystal fluorescence linewidth increases with increasing shell thickness, suggesting exciton-phonon coupling as the dominant emission line-broadening mechanism in this system. The development of the SWIR s-PCFS technique has enabled measurements of spectral linewidths of colloidal SWIR-emissive NCs in solution and provides a platform to study the single NC spectral characteristics of SWIR emitters.