  The motions of gas and stars in the nuclei of nearby large galaxies have
demonstrated that massive black holes are common and that their masses strongly
correlate with the stellar velocity dispersion $\sigma_{\star}$ of the bulge.
This correlation suggests that massive black holes and galaxies influence each
other's growth. Dynamical measurements are less reliable when the sphere of
influence is unresolved, thus it remains unknown whether this correlation
exists in galaxies much smaller than the Milky Way, as well as what fraction of
these galaxies have central black holes. Light echoes from photoionized clouds
around accreting black holes, in combination with the velocity of these clouds,
yield a direct mass measurement that circumvents this difficulty. Here we
report an exceptionally low reverberation delay of $83\pm14$ minutes between
variability in the accretion disk and high velocity H$\alpha$ emission from the
nucleus of the bulgeless dwarf galaxy NGC~4395. Combined with the H$\alpha$
line-of-sight velocity dispersion $\sigma_{\rm line}=426\pm1$~km~s$^{-1}$, this
lag determines a mass of about 10,000~$M_{\odot}$ for the black hole. This mass
is among the smallest central black hole masses reported, near the low end of
expected masses for heavy "seeds", and the best direct mass measurement for a
galaxy of this size. Despite the lack of a bulge, NGC~4395 is consistent with
the $M_{\rm BH} - \sigma_{\star}$ relation when $\sigma_{\star}$ is measured
from the central region. This indicates that the relation need not originate
from hierarchical galaxy assembly nor from black hole feedback.
