We used optical integral field spectroscopy to analyse the stellar and gas properties of the inner 1.4 kpc radius of NGC 3884, a low-luminosity active galactic nucleus (AGN) host. The observations were performed with Gemini Multi-Object Spectrograph (GMOS)-Integral Field Unit at a seeing of ~0.85 arcsec (475 pc at the galaxy) that allowed us to map the stellar and gas emission structure and kinematics, for the first time in this galaxy. The stellar motions are consistent with rotation in a disc, with the kinematic position angle (PA) ranging from approximately 0° within 500 pc to 20° beyond 1 kpc, consistent with the photometric PA. We detected extended ionized and neutral gas emission throughout most of the GMOS field of view, with three kinematic components: (i) a disc component with a kinematic PA similar to that of the stars beyond ~670 pc from the nucleus; (ii) a twist in the PA of up to 60° at a smaller radii that we attribute to gas inflow towards the nucleus; and (iii) an outflow detected as broad components to the emission lines (σ ~ 250-400 km s-1), with a maximum mass outflow rate of 0.25 ± 0.15 M⊙ yr-1 and a kinetic power corresponding to 0.06 per cent of the AGN bolometric luminosity, possibly being powerful enough to suppress star formation in the galaxy. The observed gas kinematics thus reveals both inflows and outflows in ionized gas.