  Magnetic fields in galaxies are produced via the amplification of seed
magnetic fields of unknown nature. The seed fields, which might exist in their
initial form in the intergalactic medium, were never detected. We report a
lower bound $B\ge 3\times 10^{-16}$~gauss on the strength of intergalactic
magnetic fields, which stems from the nonobservation of GeV gamma-ray emission
from electromagnetic cascade initiated by tera-electron volt gamma-ray in
intergalactic medium. The bound improves as $\lambda_B^{-1/2}$ if magnetic
field correlation length, $\lambda_B$, is much smaller than a megaparsec. This
lower bound constrains models for the origin of cosmic magnetic fields.
