We describe in this paper a measurement of vertical emittance in the Accelerator Test Facility (ATF) damping ring at KEK with a laser wire beam profile monitor. This monitor is based on the Compton scattering process of electrons with a laser light target which is produced by injecting a cw laser beam into a Fabry-Perot optical cavity. We installed the monitor at a straight section of the damping ring and measured the vertical emittance with three different ring conditions. In all cases, the ATF ring was operated at 1.28 GeV in a single bunch mode. When the ring was tuned for ultralow emittance, the vertical emittance of epsilon(y) = (1.18 +/- 0.08) x 10(-11) mrad was achieved. This shows that the ATF damping ring has realized its target value also vertically.