  Recently observational lower bounds on the strength of cosmic magnetic fields
were reported, based on gamma-ray flux from distant blazars. If inflation is
responsible for the generation of such magnetic fields then the inflation
energy scale is bounded from above as rho_{inf}^{1/4} < 2.5 times 10^{-7}M_{Pl}
times (B_{obs}/10^{-15}G)^{-2} in a wide class of inflationary magnetogenesis
models, where B_{obs} is the observed strength of cosmic magnetic fields. The
tensor-to-scalar ratio is correspondingly constrained as r< 10^{-19} times
(B_{obs}/10^{-15}G)^{-8}. Therefore, if the reported strength B_{obs} \geq
10^{-15}G is confirmed and if any signatures of gravitational waves from
inflation are detected in the near future, then our result indicates some
tensions between inflationary magnetogenesis and observations.
