Intermediate-mass black holes (103-105 M⊙) in the centre of dwarf galaxies are believed to be analogous to growing active galactic nuclei (AGNs) in the early Universe. Their characterization can provide insight about the early galaxies. We present optical and near-infrared integral field spectroscopy of the inner ˜50 pc of the dwarf galaxy NGC 4395, known to harbour an AGN. NGC 4395 is an ideal candidate to investigate the nature of dwarf AGN, as it is nearby (d ≈ 4.4 Mpc) enough to allow a close look at its nucleus. The optical data were obtained with the Gemini GMOS-IFU covering the 4500 -7300 Å spectral range at a spatial resolution of 10 pc. The J and K-band spectra were obtained with the Gemini NIFS at spatial resolutions of ˜5 pc. The gas kinematics show a compact, rotation disc component with a projected velocity amplitude of 25 km s^{-1}. We estimate a mass of 7.7 × 105 M⊙ inside a radius of 10 pc. From the Hα broad-line component, we estimate the AGN bolometric luminosity as L_bol=(9.9± 1.4)× 10^{40} erg s-1 and a mass M_BH=(2.5^{+1.0}_{-0.8})× 10^5 M⊙ for the central black hole. The mean surface mass densities for the ionized and molecular gas are in the ranges (1-2) M_{⊙} pc-2 and (1-4) × 10-3 M⊙ pc-2 and the average ratio between ionized and hot molecular gas masses is ˜500. The emission-line flux distributions reveal an elongated structure at 24 pc west of the nucleus, which is blueshifted relative to the systemic velocity of the galaxy by ≈30 km s^{-1}. We speculate that this structure is originated by the accretion of a gas-rich small satellite or by a low-metallicity cosmic cloud.