  The scaling of the specific Type Ia supernova (SN Ia) rate with host galaxy
stellar mass $\dot{N}_\text{Ia} / M_\star \sim M_\star^{-0.3}$ as measured in
ASAS-SN and DES strongly suggests that the number of SNe Ia produced by a
stellar population depends inversely on its metallicity. We estimate the
strength of the required metallicity dependence by combining the average star
formation histories (SFHs) of galaxies as a function of their stellar mass with
the mass-metallicity relation (MZR) for galaxies and common parametrizations
for the SN Ia delay-time distribution. The differences in SFHs can account for
only $\sim$30% of the increase in the specific SN Ia rate between stellar
masses of $M_\star = 10^{10}$ and $10^{7.2} M_\odot$. We find that an
additional metallicity dependence of approximately $\sim$Z$^{-0.5}$ is required
to explain the observed scaling. This scaling matches the metallicity
dependence of the close binary fraction observed in APOGEE, suggesting that the
enhanced SN Ia rate in low-mass galaxies can be explained by a combination of
their more extended SFHs and a higher binary fraction due to their lower
metallicities. Due to the shape of the MZR, only galaxies below $M_\star
\approx 3\times10^9 M_\odot$ are significantly affected by the
metallicity-dependent SN Ia rates. The $\dot{N}_\text{Ia} / M_\star \sim
M_\star^{-0.3}$ scaling becomes shallower with increasing redshift, dropping by
factor of $\sim$2 at $10^{7.2} M_\odot$ between $z = 0$ and $1$ with our
$\sim$$Z^{-0.5}$ scaling. With metallicity-independent rates, this decrease is
a factor of $\sim$3. We discuss the implications of metallicity-dependent SN Ia
rates for one-zone models of galactic chemical evolution.
