In general relativity gravitational waves propagate at the speed of light; however, in alternative theories of gravity that might not be the case. We investigate the effects of a modified speed of gravity, cT2, on the B modes of the cosmic microwave background (CMB) anisotropy in polarization. We find that a departure from the light speed value would leave a characteristic imprint on the BB spectrum part induced by tensors, manifesting as a shift in the angular scale of its peaks which allows us to constrain cT without any significant degeneracy with other cosmological parameters. We derive constraints from current data and forecast the accuracy with which cT will be measured by the next generation CMB satellites. In the former case, using the available Planck and BICEP2 data sets, we obtain cT2=1.30±0.79 and cT2<2.85 at 95% C.L. by assuming a power law primordial tensor power spectrum and cT2<2.33 at 95% C.L. if the running of the spectral index is allowed. More interestingly, in the latter case we find future CMB satellites capable of constraining cT2 at percent level, comparable with bounds from binary pulsar measurements, largely due to the absence of degeneracy with other cosmological parameters.