Proxima b is our nearest potentially rocky exoplanet and represents a formidable opportunity for exoplanet science and possibly astrobiology. With an angular separation of only 35 mas (or 0.05 AU) from its host star, Proxima b is however hardly observable with current imaging telescopes and future space-based coronagraphs. One way to separate the photons of the planet from those of its host star is to use an interferometer that can easily resolve such spatial scales. In addition, its proximity to Earth and its favorable contrast ratio compared with its host M dwarf (approximately 10^-5 at 10 microns) makes it an ideal target for a space-based nulling interferometer with relatively small apertures. In this paper, we present the motivation for observing this planet in the mid-infrared (5-20 microns) and the corresponding technological challenges. Then, we describe the concept of a space-based infrared interferometer with relatively small (<1m in diameter) apertures that can measure key details of Proxima b, such as its size, temperature, climate structure, as well as the presence of important atmospheric molecules such as H₂O, CO₂, O₃, and CH₄. Finally, we illustrate the concept by showing realistic observations using synthetic spectra of Proxima b computed with coupled climate chemistry models.