We present matter-wave interferometry as a tool to advance spectroscopy for a wide class of nanoparticles, clusters and molecules. The high sensitivity of de Broglie interference fringes to external perturbations enables measurements in the limit of an individual particle absorbing only a single photon on average, or even no photon at all. The method allows one to extract structural and electronic information from the loss of the interference contrast. It is minimally invasive and works even for dilute ensembles.