We present stellar and gaseous kinematics of the inner ≈350-pc radius of the Seyfert galaxy Mrk 1066 derived from J and Kl bands data obtained with the Gemini’s Near-Infrared Integral Field Spectrograph (NIFS) at a spatial resolution of ≈35 pc. The stellar velocity field is dominated by rotation in the galaxy plane but shows an S-shape distortion along the galaxy minor axis which seems to be due to an oval structure seen in an optical continuum image. Along this oval, between 170 and 280 pc from the nucleus we find a partial ring of low σ* (≈50 km s−1) attributed to an intermediate-age stellar population. The velocity dispersion of the stellar bulge (σ*≈ 90 km s−1) implies a supermassive black hole mass of ≈5.4 × 106 M⊙. From measurements of the emission-line fluxes and profiles ([P ii]λ 1.1886 μm, [Fe ii]λ 1.2570 μm, Paβ and H2λ 2.1218 μm), we have constructed maps for the gas centroid velocity, velocity dispersion as well as channel maps. The velocity fields for all emission lines are dominated by a similar rotation pattern to that observed for the stars, but are distorted by the presence of two structures: (i) a compact rotating disc with radius r≈ 70 pc; (ii) outflows along the radio jet which is oriented approximately along the galaxy major axis. The compact rotating disc is more conspicuous in the H2 emitting gas, which presents the smallest σ values (≤70 km s−1) and most clear rotation pattern, supporting a location in the galaxy plane. We estimate a gas mass for the disc of ∼107 M⊙. The H2 kinematics further suggests that the nuclear disc is being fed by gas coming from the outer regions. The outflow is more conspicuous in the [Fe ii] emitting gas, which presents the highest σ values (up to 150 km s−1) and the highest blue and redshifts of up to 500 km s−1, while the highest stellar rotation velocity is only ≈130 km s−1. We estimate a mass-outflow rate in ionized gas of ≈6 × 10−2 M⊙ yr−1. The derived kinematics for the emitting gas is similar to that observed in previous studies supporting that the H2 is a tracer of the active galactic nucleus feeding and the [Fe ii] of its feedback.