Nuclear isomer effects are pivotal in understanding nuclear astrophysics, particularly in the rapid neutron-capture process where the population of metastable isomers can alter the radioactive decay paths of nuclei produced during astrophysical events. The β-decaying isomer ^{128m}Sb was identified as potentially impactful since the β-decay pathway along the A=128 isobar funnels into this state bypassing the ground state. We report the first direct mass measurements of the ^{128}Sb isomer and ground state using the Canadian Penning Trap mass spectrometer at Argonne National Laboratory. We find mass excesses of -84564.8(25) keV and -84608.8(21) keV, respectively, resulting in an excitation energy for the isomer of 43.9(33) keV. These results provide the first key nuclear data input for understanding the role of ^{128m}Sb in nucleosynthesis, and we show that it will influence the flow of the rapid neutron-capture process.