We demonstrate that dwarf galaxies (10 super(7) < M sub(stellar) < 10 super(9) M sub(middot in circle), -12 < M sub(r) > -18) with no active star formation are extremely rare (<0.06%) in the field. We examine the relative number of quenched versus star-forming dwarf galaxies, defining quenched galaxies as having no Halpha emission (EW sub(H)alpha < 2 A) and a strong 4000 A break. The fraction of quenched dwarf galaxies decreases rapidly with increasing distance from a massive host, leveling off for distances beyond 1.5 Mpc. We define galaxies beyond 1.5 Mpc of a massive host galaxy to be in the field. We demonstrate that there is a stellar mass threshold of M sub(stellar) < 1.0 x 10 super(9) M sub(middot in circle) below which quenched galaxies do not exist in the field. The majority of quenched dwarf galaxies (often classified as dwarf elliptical galaxies) are within 2 virial radii of a massive galaxy, and only a few percent of quenched dwarf galaxies exist beyond 4 virial radii.