The presence of disorder in a non-interacting system can localize all energy eigenstates, a phenomena well-known as Anderson localization. Many-body localization is an extension of this effect which includes interactions, and has attracted considerable attention recently. We propose to apply spin noise spectroscopy (SNS) to detect many-body localization in disordered spin systems. These SNS methods are relatively non-invasive technique to probe spontaneous spin fluctuations. We show that the spin noise signals obtained by cross-correlation SNS with two probe beams can be used to separate the many-body localized phase from a noninteracting Anderson localized phase and a delocalized (diffusive) phase in the studied models for which we numerically calculate real time spin noise signals and their power spectra. For the archetypical case of the disordered XXZ spin chain we also develop a simple phenomenological model.