We present the results of a recent reverberation mapping campaign for UGC 06728 , a nearby low-luminosity Seyfert 1 in a late-type galaxy . Nightly monitoring in the spring of 2015 allowed us to determine an H \beta time delay of \tau = 1.4 \pm 0.8 days . Combined with the width of the variable H \beta line profile , we determine a black hole mass of M _ { BH } = ( 7.1 \pm 4.0 ) \times 10 ^ { 5 } M _ { \odot } . We also constrain the bulge stellar velocity dispersion from higher-resolution long slit spectroscopy along the galaxy minor axis and find \sigma _ { \star } = 51.6 \pm 4.9 km s ^ { -1 } . The measurements presented here are in good agreement with both the R _ { BLR } - L relationship and the M _ { BH } - \sigma _ { \star } relationship for AGNs . Combined with a previously published spin measurement , our mass determination for UGC 06728 makes it the lowest-mass black hole that has been fully characterized , and thus an important object to help anchor the low-mass end of black hole evolutionary models .