We report the discovery of NGTS-4b, a sub-Neptune-sized planet transiting a 13th magnitude K-dwarf in a 1.34 d orbit. NGTS-4b has a mass M = 20.6 ± 3.0 M⊕ and radius R = 3.18 ± 0.26 R⊕, which places it well within the so-called ‘Neptunian Desert’. The mean density of the planet (3.45 ± 0.95 g cm−3) is consistent with a composition of 100 per cent H2O or a rocky core with a volatile envelope. NGTS-4b is likely to suffer significant mass loss due to relatively strong EUV/X-ray irradiation. Its survival in the Neptunian desert may be due to an unusually high-core mass, or it may have avoided the most intense X-ray irradiation by migrating after the initial activity of its host star had subsided. With a transit depth of 0.13 ± 0.02 per cent, NGTS-4b represents the shallowest transiting system ever discovered from the ground, and is the smallest planet discovered in a wide-field ground-based photometric survey.