Context. The Virgo cluster is the nearest (d = 16.5 Mpc) massive (M ≥ 10 M) galaxy cluster and is therefore a prime target for studying astrophysical processes in dense large-scale environments. In the radio band, we can probe the nonthermal components of the interstellar medium, the intracluster medium (ICM), and of active galactic nuclei (AGN). This allows an investigation of the impact of the environment on the evolution of galaxies and the contribution of AGN to ICM heating. With the ViCTORIA (VIrgo Cluster multi-Telescope Observations in Radio of Interacting galaxies and AGN) project, we are carrying out multiple wide-field surveys of the Virgo cluster at different frequencies. Aims. We aim to investigate the impact of the environment on the evolution of galaxies and the contribution of AGN to ICM heating – from the inner cluster regions out to beyond the virial radius. Methods. We performed a survey of the cluster at 120–168 MHz using the LOw-Frequency ARray (LOFAR). We imaged a 132 deg region of the cluster, reaching an order-of-magnitude greater sensitivity than existing wide-field radio surveys of this field at three times higher spatial resolution compared to other low-frequency observations. We developed a tailored data processing strategy to subtract the bright central radio galaxy M 87 from the data. This allowed us to correct for systematic effects due to ionospheric variation as a function of time and direction. Results. In the final mosaic, which has a resolution of 9'' 5'', we reach a median noise level of 140 μJy beam inside the virial radius and 280 μJy beam for the full area. We detect 112 Virgo member galaxies and 114 background galaxies. In at least 18 cases, the radio morphology of the cluster member galaxies shows clear signs of ram-pressure stripping. This includes three previously unreported candidates. In addition, we reveal previously undiscovered tails of 150 kpc in length from a previous epoch of AGN activity for NGC 4472 (M 49). While no cluster-scale diffuse radio sources are discovered, we find the presence of an extended radio signature of the W′ group. This feature is coincident with an X-ray filament detected with SRG/eROSITA in the outskirts of the cluster. We speculate that this emission is synchrotron radiation, which could be related to shocks or turbulence from accretion processes. Conclusions. The data published in this paper serve as a valuable resource for future studies. In the follow-up work of the ViCTORIA project, we will use these data for an analysis of environmental effects on the radio properties of star-forming galaxies in Virgo.