In this letter we discuss the implications of causality on a primordial magnetic field. We show that the residual field on large scales is much stronger suppressed than usually assumed and that a helical component is even suppressed even more than the parity even part. We show that due to this strong suppression, even maximal primordial fields generated at the electroweak phase transition can just marginally seed the fields in galaxies and clusters, but they cannot leave any detectable imprint on the cosmic microwave background.