Anastrepha grandis (Macquart) (Diptera: Tephritidae) is endemic to the lowland Andean region of South America and considered a quarantine pest of cucurbits by most tropical and subtropical countries outside of the infested region. Despite its regulatory significance, the only phytosanitary treatment available is a generic phytosanitary irradiation dose of 150 Gy that is accepted for all Tephritidae but that was developed without any data on radiotolerance of A. grandis. The objectives of this research were to determine the most cold-tolerant developmental stage of A. grandis and to estimate a time period required for a phytosanitary cold treatment in zucchini squash, Cucurbita pepo L. (Cucurbitaceae). The most cold-tolerant developmental stage of A. grandis in fruit was the 3rd instar, and the time required for a phytosanitary cold treatment in zucchini squash when treated at a minimum of 1.0 °C was estimated at ~23 d. This indicates that A. grandis is approximately as cold tolerant as the most cold-tolerant Anastrepha species known, i.e., Anastrepha ludens (Loew). However, in small-scale testing, no survivors were found at 14 d (n = 340) and the estimated time of 23 d needs to be confirmed by large-scale testing before it should be used commercially. As statistical estimates of extreme values (>99.9%) are not very reliable, and data from 3rd instars did not fit the model well, large-scale testing should be initiated at a treatment time <23 d to not result in an excessive commercial treatment dose.