Context. According to radiative models, radio galaxies may produce γ-ray emission from the first stages of their evolution. However, very few such galaxies have been detected by the Fermi Large Area Telescope (LAT) so far. Aims. NGC 3894 is a nearby (z = 0.0108) object that belongs to the class of compact symmetric objects (CSOs, i.e., the most compact and youngest radio galaxies), which is associated with a γ-ray counterpart in the Fourth Fermi-LAT source catalog. Here we present a study of the source in the γ-ray and radio bands aimed at investigating its high-energy emission and assess its young nature. Methods. We analyzed 10.8 years of Fermi-LAT data between 100 MeV and 300 GeV and determined the spectral and variability characteristics of the source. Multi-epoch very long baseline array (VLBA) observations between 5 and 15 GHz over a period of 35years were used to study the radio morphology of NGC 3894 and its evolution. Results. NGC 3894 is detected in γ-rays with a significance >9σ over the full period, and no significant variability has been observed in the γ-ray flux on a yearly time-scale. The spectrum is modeled with a flat power law (Γ = 2.0 ± 0.1) and a flux on the order of 2.2 × 10⁻⁹ ph cm⁻² s⁻¹. For the first time, the VLBA data allow us to constrain with high precision the apparent velocity of the jet and counter-jet side to be β_{app, NW} = 0.132 ± 0.004 and β_{app, SE} = 0.065 ± 0.003, respectively. Conclusions. Fermi-LAT and VLBA results favor the youth scenario for the inner structure of this object, with an estimated dynamical age of 59 ± 5 years. The estimated range of viewing angle (10° < θ < 21°) does not exclude a possible jet-like origin of the γ-ray emission.