Abstract Field dwarf galaxies not actively forming stars are relatively rare in the local Universe, but are present in cosmological hydrodynamical simulations. We use the TNG50 simulation to investigate their origin and find that they all result from environmental effects that have removed or reduced their gas content. Quenched field dwarfs consist of either backsplash objects ejected from a massive host or of systems that have lost their gas after crossing overdense regions such as filaments or sheets (“cosmic web stripping”). Quenched fractions rise steeply with decreasing stellar mass, with quenched systems making up roughly ∼15% of all field dwarfs (i.e., excluding satellites) with stellar masses 107 < M ⋆/M ⊙ < 109. This fraction drops to only ∼1% when a strict isolation criterion that requires no neighbors with M ⋆ > 109 M ⊙ within 1.5 Mpc is applied. Of these isolated dwarfs, ∼6% are backsplash, while the other ∼94% have been affected by the cosmic web. Backsplash systems are more deficient in dark matter, have retained less or no gas, and have stopped forming stars earlier than cosmic web-stripped systems. The discovery of deeply isolated dwarf galaxies that were quenched relatively recently would lend observational support to the prediction that the cosmic web is capable of inducing the cessation of star formation in dwarfs.