We investigate both theoretically and experimentally the effects of Brillouin-induced dispersion on modulated Stokes light, in all regimes of modulation frequency, while allowing for Stokes center-frequency detuning from the Brillouin resonance.  Previously published work has only treated the case of a resonant Stokes. Stokes detuning introduces a surprising result:  Even for GHz modulation frequencies, which are significantly beyond the Brillouin bandwidth of 20 MHz, an extremely sharp spectral dependency (a spectral hole) of the modulated Stokes amplitude and phase appears, with an optical bandwidth on the order of 1-10 Hz. This new and dramatic effect would be interesting for microwave photonic signal processing, optical frequency monitoring and Brillouin-based fiber sensors.