Soursop (Annona muricata L.) is climacteric fruit with a short ripening period and postharvest shelf life, leading to a rapid softening. In this study, transcriptome analysis of soursop fruits was performed to identify key gene families involved in ripening under postharvest storage conditions (Day 0, Day 3 stored at 28 ± 2 °C, Day 6 at 28 ± 2 °C, Day 3 at 15 ± 2 °C, Day 6 at 15 ± 2 °C, Day 9 at 15 ± 2 °C). The transcriptome analysis showed 224,074 transcripts assembled clustering into 95, 832 unigenes, of which 21, 494 had ORF. RNA-seq analysis showed the highest number of differentially expressed genes on Day 9 at 15 ± 2 °C with 9291 genes (4772 up-regulated and 4519 down-regulated), recording the highest logarithmic fold change in pectin-related genes. Enrichment analysis presented significantly represented GO terms and KEGG pathways associated with molecular function, metabolic process, catalytic activity, biological process terms, as well as biosynthesis of secondary metabolites, plant hormone signal, starch, and sucrose metabolism, plant–pathogen interaction, plant–hormone signal transduction, and MAPK-signaling pathways, among others. Network analysis revealed that pectinesterase genes directly regulate the loss of firmness in fruits stored at 15 ± 2 °C.