We present two-dimensional (2D) gas kinematics and excitation of the inner 300 pc of the Seyfert galaxy ES0428-G14 at a sampling of 14 pc 2 , from near-infrared spectroscopic observations at R ≈ 6000 obtained with the Integral Field Unit (IFU) of the Gemini Near-Infrared Spectrograph. From measurements of fluxes and profiles of the emission lines [Fe II]λ 1.257 μm, Paβ, H 2 λ 2.121 μm and Bry, we construct 2D maps of line intensities and ratios, radial velocities and velocity dispersions. Emission line 'tomography' is provided by velocity slices obtained across the line profiles, a unique capability of IFUs, which allows the mapping of not only the peak velocities but including also the wings. We compare these maps with a previously published high spatial resolution radio map and find a tight relation between the radio structure and the emission-line flux distributions and kinematics, revealing that the radio jet plays a fundamental role not only in shaping the narrow-line region but also in the imprint of its kinematics. Blueshifts of up to 400 km s -1 and velocity dispersions of up to 150 km s -1 are observed in association with the radio jet at a position angle (PA) = 129°, which is also the PA of the photometric major axis of the galaxy. We conclude that the radio jet is launched at a small angle relative to the galactic plane, with the north-western side slightly oriented towards us. This angle is small enough for the radio jet to shock and compress the gas in the plane of the galaxy, and for the nuclear continuum to ionize and heat it. The distinct kinematics and flux distributions observed for the different emission lines suggest different origins for their emission. The [Fe ΙΙ] shows the largest blueshifts and velocity dispersions and its flux distribution is concentrated along the jet, while the H 2 shows the lowest velocity dispersions and has additional flux contribution from regions beyond the jet. Both X-rays emitted by the active galactic nucleus and shocks produced by the radio jet can excite the H 2 and [Fe II] emission lines. We use the 2D velocity dispersion maps to estimate upper limits to the contribution of the radio jet to the excitation of [Fe n] and H 2 which may reach 90 per cent for [Fe II] and 80 per cent for H 2 in the jet region. The [Fe II]/Paβ emission-line ratios and the association of the [Fe ΙΙ] flux distribution and kinematics with the radio structure support a stronger contribution of the radio jet to the [Fe ΙΙ] excitation than that of H 2 . In the regions beyond the jet, the observations favour X-ray excitation.