The spectral response of a Bragg grating reflector inscribed in a microstructured optical fibre is tuned by employing an infiltrated ferrofluid, while modifying the overlap of the ferrofluidic medium with the grating length. Significant spectral changes in terms of Bragg grating wavelength shift and extinction ratio were obtained under static magnetic field actuation. Spectral measurements revealed non-bidirectional propagation effects dependent upon the relative position between the ferrofluid and the grating. The actuation speed of the device was measured to be of the order of few seconds.