The ground-state-to-ground-state β-decay Q value of ^{135}Cs(7/2^{+})→^{135}Ba(3/2^{+}) has been directly measured for the first time. The measurement was done utilizing both the phase-imaging ion-cyclotron resonance technique and the time-of-flight ion-cyclotron resonance technique at the JYFLTRAP Penning-trap setup and yielded a mass difference of 268.66(30) keV between ^{135}Cs(7/2^{+}) and ^{135}Ba(3/2^{+}). With this very small uncertainty, this measurement is a factor of 3 more precise than the currently adopted Q value in the Atomic Mass Evaluation 2016. The measurement confirms that the first-forbidden unique β^{-}-decay transition ^{135}Cs(7/2^{+})→^{135}Ba(11/2^{-}) is a candidate for antineutrino mass measurements with an ultralow Q value of 0.44(31) keV. This Q value is almost an order of magnitude smaller than those of nuclides presently used in running or planned direct (anti)neutrino mass experiment.