Zucchini fruit (Cucurbita pepo L.) is susceptible to chilling injury (CI) during its postharvest life, with this response being cultivar-dependent. A previous transcriptomic analysis comparing cold-tolerant fruit from the cultivar ‘Natura’ with cold-sensitive fruit from the cultivar ‘Sinatra’, revealed the transcription factor (TF) CpMYB106-like as a relevant candidate gene for the acquisition of postharvest low-temperature tolerance. C. pepo has two CpMYB106-like paralogs, which are differentially present in the ‘Natura’ (CpMYB106-likeA) and ‘Sinatra’ (CpMYB106-likeB) cultivars due to gene and promoter deletions. The aim of this study was to investigate the transcriptional regulation of the CpMYB106-like paralogs to unravel their role in the postharvest life of zucchini fruit. For this, gene expression was analyzed and promoter sequences and their activities were studied through reporter β-glucuronidase (GUS) gene analysis in heterologous systems. An expression analysis showed that CpMYB106-like mRNA levels were induced only in the cold-stored fruit of ‘Natura’. The analysis of the promoter sequences showed numerous cis-regulatory elements (CREs), many of which have a differential distribution or frequency between the two paralogs. Promoter basal activity was determined by transient transformation of Nicotiana benthamiana leaves, which showed a higher expression driven by the promoter from the cold-tolerant cultivar ‘Natura’, which could be explained by the presence of three additional copies of the enhancer element EECCRCAH1 in proMYB106A. The tissue-specific expression pattern, and the response to abiotic stresses and phytohormones controlled by CpMYB106-like promoters was analyzed in transgenic Arabidopsis thaliana plants. GUS activity was mainly detected in the vascular system, leaves, and inflorescences, especially in siliques. With respect to abiotic stresses, low temperature decreased GUS expression in Arabidopsis, but increased it in plants carrying the ‘Natura’ promoter after a 24-h acclimation period at 22 °C. Salt treatment induced GUS activity driven by both promoters in Arabidopsis seedlings, but it was higher with the ‘Natura’ promoter. Furthermore, methyl jasmonate (MeJA) also induced a sharp increase of GUS controlled by proMYB106A. These results suggest that the regulation of CpMYB106-like TFs in zucchini is promoter-driven, and reveal the involvement of these genes in the acquisition of cold tolerance in fruit during postharvest stress conditions.