  As additional perturbative degrees of freedom, it is known that magnetic
fields of inflationary origin can source curvature perturbations on
super-Hubble scales. By requiring the magnetic generated curvature to remain
smaller than its inflationary adiabatic counterpart during inflation and
reheating, we derive new constraints on the maximal field value today, the
reheating energy scale and its equation of state parameter. These bounds end up
being stronger by a few order of magnitude than those associated with a
possible backreaction of the magnetic field onto the background. Our results
are readily applicable to any slow-roll single field inflationary models and
any magnetic field having its energy density scaling as a^gamma during
inflation. As an illustrative example, massive inflation is found to remain
compatible with a magnetic field today Bo = 5 x 10^(-15) G for some values of
gamma only if a matter dominated reheating takes place at energies larger than
10^5 GeV. Conversely, assuming gamma=-1, massive inflation followed by a matter
dominated reheating cannot explain large scale magnetic fields larger than
10^(-20) G today.
