Members of the multiple organellar RNA editing factor (MORF) gene family play indispensable roles in regulating chloroplast development, plant growth, and responses to abiotic stress. However, their functions in potato (Solanum tuberosum) remain unclear. In this study, a total of eight StMORF members were identified in potato, distributed across seven chromosomes. Following phylogenetic classification of the StMORF genes into five major clades, subsequent investigations included their exon–intron architecture, conserved protein motifs, collinearity across related species, and predicted interaction networks. Selected interactions among StMORF proteins were experimentally validated by Y2H, and their expression levels in different tissues were assessed. All StMORF members exhibited high expression in leaves. Additionally, analyses of promoter cis-acting elements and RNA-seq data from the Potato Genome Sequencing Consortium (PGSC) database indicated that the StMORF gene family may play important roles in potato’s responses to abiotic stress. Quantitative real-time PCR (qRT-PCR) validation results were largely consistent with transcriptomic data, confirming that several StMORF genes are involved in abiotic stress responses. This study provides a comprehensive analysis of the StMORF gene family and lays a foundation for further exploration of its physiological functions in potato.