Spectroscopic microtomography provides the ability to perform 4D (3D structural and 1D chemical) imaging of a thick microscopic specimen. Here, we demonstrate spectroscopic microtomography in the short-wave infrared (SWIR) wavelength using digital holographic tomography, which captures both the absorption coefficient and refractive index. A broadband laser in tandem with a tunable optical filter allows us to scan the wavelength from 1100 to 1650 nm. Using the developed system, we measure human hair and sea urchin embryo samples. The resolution estimated with gold nanoparticles is 1.51μm (transverse) and 1.57μm (axial) for the field of view of 307 × 246μm2. The developed technique will enable accurate and efficient analyses of microscopic specimens that have a distinctive absorption or refractive index contrast in the SWIR range.