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 > or = 3 x 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 rays in intergalactic medium. The bound improves as lambdaB(-1/2) if magnetic field correlation length, lambdaB, is much smaller than a megaparsec. This lower bound constrains models for the origin of cosmic magnetic fields.