Ocean flow moves sea water through the Earth's magnetic field, inducing electric fields, currents and secondary magnetic fields. These motionally induced magnetic fields have a potential for the remote sensing of ocean flow variability. A first goal must be to gain a better understanding of magnetic field generation by tidal ocean flow. We predict the motionally induced magnetic fields for the six major tidal constituents and compare their amplitudes with the spectra of night time observatory and satellite magnetic measurements for the Indian Ocean. The magnetic variations at the solar S2, K1, and P1 periods turn out to be dominated by unrelated external fields. In contrast, observed lunar M2 and N2 tidal signals are in fair agreement with predictions from motional induction. The lunar diurnal O1 signal, visible at some observatories, could be caused by ocean flow but disagrees in amplitude with our predictions.