The eclipsing binary system 2M 1938+4603 consists of a pulsating hot subdwarf B star and a cool M dwarf companion in an effectively circular three-hour orbit. The light curve shows both primary and secondary eclipses, along with a strong reflection effect from the cool companion. Here we present constraints on the component masses and eccentricity derived from the R{\o}mer delay of the secondary eclipse. Using six months of publicly-available Kepler photometry obtained in Short Cadence mode, we fit model profiles to the primary and secondary eclipses to measure their centroid values. We find that the secondary eclipse arrives on average 2.06 +/- 0.12 s after the midpoint between primary eclipses. Under the assumption of a circular orbit, we calculate from this time delay a mass ratio of q = 0.2691 +/- 0.0018 and individual masses of M_sd = 0.372 +/- 0.024 Msun and M_c = 0.1002 +/- 0.0065 Msun for the sdB and M dwarf, respectively. These results differ slightly from those of a previously-published light curve modeling solution; this difference, however, may be reconciled with a very small eccentricity, e cos \omega\ ~ 0.00004. We also report an orbital period decrease of P-dot = (-1.23 +/- 0.07) x 10^-10.