We propose a method for high-sensitivity subwavelength spectromicroscopy based on the usage of a spaser (plasmonic nanolaser) in the form of a scanning probe microscope tip. The high spatial resolution is defined by plasmon localization at the tip, as is the case for apertureless scanning near-field optical microscopy. In contrast to the latter method, we suggest using radiationless plasmon pumping with quantum dots instead of irradiation with an external laser beam. Due to absorption at the transition frequencies of neighboring nano-objects (molecules or clusters), dips appear in the plasmon generation spectrum. The highest sensitivity is achieved near the generation threshold.