We report the first search for the K_L →π^0 γ decay, which is forbidden by Lorentz invariance, using the data from 2016 to 2018 at the J-PARC KOTO experiment. With a single event sensitivity of (7.1± 0.3_ stat.± 1.6_ syst.)× 10^-8, no candidate event was observed in the signal region. The upper limit on the branching fraction was set to be 1.7× 10^-7 at the 90% confidence level.