The motions of gas and stars in the nuclei of nearby galaxies have demonstrated that massive black holes are common1 and that their masses correlate with the stellar velocity dispersion σ★ of the bulge2-4. This correlation suggests that massive black holes and galaxies influence each other's growth5-7. 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. Light echoes from photoionized clouds around accreting black holes8,9, 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 ± 14 min between variability in the accretion disk and Hα emission from the nucleus of the dwarf galaxy NGC 4395. Combined with the Hα velocity dispersion σline = 426 ± 1 km s-1, this lag determines a mass of about 10,000 M⊙ for the black hole (MBH). This mass is among the smallest central black hole masses reported, near the low end of expected masses for heavy `seeds'10-12, and the best direct mass measurement for a galaxy of this size. Despite the lack of a bulge, NGC 4395 is consistent with the MBH-σ★ relation, indicating that the relation need not originate from hierarchical galaxy assembly nor from black hole feedback.