The identification and quantification of Glucosinolates (Gls) via UPLC® MS-MS/PDA/qToF in ten mashua cultivars was carried out. Gls total contents were within the 4.9–54.2 μmol g−1 dry matter range, of which 96–99% corresponded to glucoaubrietin. Other less abundant Gls were glucotropaeolin and tentatively two isomers of hydroxybenzyl Gls. Postharvest refrigeration and shade storage conditions increased the content of Gls up to day 6 in 39.7% and 51.5% respectively. Sun exposure increased the Gls content in 40% up to day 3 but from day 6 considerable losses were attained (92% at day 15). Low correlation levels (R2) between the Gls and myrosinase (MYR) activity of 0.57, 0.28 and 0.39 for the refrigeration, shade and sun exposure treatments were obtained. The cooking regimes tested, boiling, microwaving and baking totally inactivated MYR without affecting the Gls content.