Chenopodium hircinum, the putative wild ancestor of quinoa, is a source of traits that could improve the tolerance of crop quinoa to high temperatures. However, seeds of C. hircinum have physiological dormancy (PD), which is an obstacle for plant propagation and use in breeding programs. We studied the intraspecific variability in morpho-anatomical traits of embryo covering structures and their association with PD. We also evaluated the effects of different dormancy-breaking treatments on PD alleviation and germination. Seeds were dispersed with a remnant perianth and a persistent pericarp that could be removed by scraping. The seed coat was formed by palisade cells impregnated with tannins, and the seed contained a thin layer of peripheral endosperm surrounding the embryo. In our investigation, the thickness of the pericarp (P) and/or seed coat (SC) varied among populations. Populations with higher P and/or SC thickness showed lower percentages of germination and water absorption. The combined dormancy-breaking treatment (bleach + perforated coverings + gibberellic acid) promoted dormancy release and increased germination. C. hircinum seeds showed non-deep physiological dormancy. Based on previous knowledge about quinoa, and our results, we conclude that embryo coverings, especially the seed coat, have an important role in dormancy control, imposing a mechanical restraint on radicle emergence.