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