The Next Generation Virgo Cluster Survey is a deep (with a 2σ detection limit μ_g = 29 mag arcsec^(−2) in the g-band) optical panchromatic survey targeting the Virgo cluster from its core to virial radius, for a total areal coverage of 104 square degrees. As such, the survey is well suited for the study of galaxies' outskirts, haloes, and low surface brightness features that arise from dynamical interactions within the cluster environment. We report the discovery of extremely faint (μ_g > 25 mag arcsec^(−2)) shells in three Virgo cluster early-type dwarf galaxies: VCC 1361, VCC 1447, and VCC 1668. Among them, VCC 1447 has an absolute magnitude M_g = −11.71 mag and is the least massive galaxy with a shell system discovered to date. We present a detailed study of these low surface brightness features. We detect between three and four shells in each of our galaxies. Within the uncertainties, we find no evidence of a color difference between the galaxy main body and shell features. The observed arcs of the shells are located up to several effective radii of the galaxies. We further explore the origin of these low surface brightness features with the help of idealized numerical simulations. We find that a near equal mass merger is best able to reproduce the main properties of the shells, including their quite symmetric appearance and their alignment along the major axis of the galaxy. The simulations provide support for a formation scenario in which a recent merger, between two near-equal mass, gas-free dwarf galaxies, forms the observed shell systems.