  Magnetic fields large enough to be observable are ubiquitous in astrophysics,
even at extremely large length scales. This has led to the suggestion that such
fields are seeded at very early (inflationary) times, and subsequently
amplified by various processes involving, for example, dynamo effects. Many
such mechanisms give rise to extremely large magnetic fields at the end of
inflationary reheating, and therefore also during the quark-gluon plasma epoch
of the early universe. Such plasmas have a well-known holographic description
in terms of a thermal asymptotically AdS black hole. We show that holography
imposes an upper bound on the intensity of magnetic fields ($\approx \; 3.6
\times 10^{18}\;\; \text{gauss}$ at the hadronization temperature) in these
circumstances; this is above, but not far above, the values expected in some
models of cosmic magnetogenesis.
