The nearby dwarf spiral galaxy NGC 4395 contains a broad-lined active galactic nucleus (AGN) of exceptionally low luminosity powered by accretion onto a central black hole of very low mass (\(\sim10^4-10^5\) M\(_\odot\)). In order to constrain the size of the optical continuum emission region through reverberation mapping, we carried out high-cadence photometric monitoring of NGC 4395 in the \(griz\) filter bands on two consecutive nights in 2022 April using the four-channel MuSCAT3 camera on the Faulkes Telescope North at Haleakal\={a} Observatory. Correlated variability across the \(griz\) bands is clearly detected, and the \(r\), \(i\), and \(z\) band light curves show lags of \(8.4^{+1.0}_{-1.1}\), \(14.2^{+1.2}_{-1.4}\), and \(20.4^{+2.0}_{-2.1}\) minutes with respect to the \(g\) band when measured using the full-duration light curves. When lags are measured for each night separately, the Night 2 data exhibit lower cross-correlation amplitudes and shorter lags than the Night 1 light curves. Using the full-duration lags, we find that the lag-wavelength relationship is consistent with the \(\tau\propto\lambda^{4/3}\) dependence found for more luminous AGN. Combining our results with continuum lags measured for other objects, the lag between \(g\) and \(z\) band scales with optical continuum luminosity as \(\tau_{gz} \propto L^{0.56\pm0.05}\), similar to the scaling of broad-line region size with luminosity, reinforcing recent evidence that diffuse continuum emission from the broad-line region may contribute substantially to optical continuum variability and reverberation lags.