We report cumulants of the proton multiplicity distribution from dedicated fixed-target Au+Au collisions at sqrt[s_{NN}]=3.0 GeV, measured by the STAR experiment in the kinematic acceptance of rapidity (y) and transverse momentum (p_{T}) within -0.5<y<0 and 0.4<p_{T}<2.0 GeV/c. In the most central 0%-5% collisions, a proton cumulant ratio is measured to be C_{4}/C_{2}=-0.85±0.09 (stat)±0.82 (syst), which is 2σ below the Poisson baseline with respect to both the statistical and systematic uncertainties. The hadronic transport UrQMD model reproduces our C_{4}/C_{2} in the measured acceptance. Compared to higher energy results and the transport model calculations, the suppression in C_{4}/C_{2} is consistent with fluctuations driven by baryon number conservation and indicates an energy regime dominated by hadronic interactions. These data imply that the QCD critical region, if created in heavy-ion collisions, could only exist at energies higher than 3 GeV.