Acousto-optic modulation of a 1 cm fiber Bragg grating at 10.9 MHz frequency and 1065 nm wavelength is demonstrated for the first time. A special modulator design is employed to acoustically induce a dynamic radial long period grating which couples power of the fundamental mode to the higher-order modes supported by the Bragg grating. A modulated reflection band with a depth of 16 dB and 320 pm bandwidth has been achieved. The results indicate a higher modulation frequency compared to previous studies using flexural acoustic waves. In addition, the reduction of the grating length and the modulator size points to compact and faster acousto-optic modulators.