We demonstrate the spectroscopy of incoherent light with subdiffraction resolution. In a proof-of-principle experiment, we analyze the spectrum of a pair of incoherent pointlike sources whose separation is below the diffraction limit. The two sources mimic a planetary system, with a brighter source for the star and a dimmer one for the planet. Acquiring spectral information about the secondary source is difficult because the two images have a substantial overlap. This limitation is solved by leveraging a structured measurement based on spatial-mode demultiplexing, where light is first sorted in its Hermite–Gaussian components in the transverse field then measured by photon detection. This allows us to effectively decouple the photons coming from the two sources. An application is suggested to enhance the exoplanets’ atmosphere spectroscopy. A number of experiments of super-resolution imaging based on spatial demultiplexing have been conducted in the past few years, with promising results. Here, for the first time to the best of our knowledge, we extend this concept to the domain of spectroscopy.