  Fast Radio Bursts (FRBs) are a mysterious flash phenomenon detected in radio
wavelengths with a duration of only a few milliseconds, and they may also have
prompt gamma-ray flashes. Here we carry out a blind search for msec-duration
gamma-ray flashes using the 7-year Fermi Large Area Telescope (Fermi-LAT)
all-sky gamma-ray data. About 100 flash candidates are detected, but after
removing those associated with bright steady point sources, we find no flash
events at high Galactic latitude region (|b|>20 deg). Events at lower latitude
regions are consistent with statistical flukes originating from the diffuse
gamma-ray background. From these results, we place an upper limit on the GeV
gamma-ray to radio flux ratio of FRBs as xi \equiv (nu L_nu)_gamma / (nu
L_nu)_radio < 10^8, depending on the assumed FRB rate evolution. This limit is
comparable with the largest value found for pulsars, though xi of pulsars is
distributed in a wide range. We also compare this limit with the spectral
energy distribution of the 2004 giant flare of the magnetar SGR 1806-20.
