Cytokinin (CK) is an important hormone that regulates cell differentiation. The CK content in plants is regulated by cytokinin oxidase (CKX), an important enzyme that participates in hormone-regulated pathways. Additionally, CKXs comprise a large family of enzymes, but little information exists on the CKXs in potato (Solanum tuberosum). In this study, nine CKXs were identified in the potato genome and named StCKX01-09, according to their order on the linkage groups (LGs). They belong to six subfamilies, and the members within the respective subfamilies had similar motifs, a similar gene structure, and similar cis-acting elements. Additionally, the CKXs from four other species, including Arabidopsis, rice (Oryza sativa), soybean (Glycine max), and maize (Zea mays), were also divided into six subfamilies, while members within each subfamily had similar types of motifs. Moreover, the potato StCKXs were shown to influence plant hormones and stress-related factors. StCKXs were collinear, with one CKX in Arabidopsis and five CKXs in Glycine max. Quantitative real-time PCR (qRT-PCR) revealed tissue-specific expression patterns in the potato seedlings and changes in the expression levels in response to stress. Furthermore, the cytokinin content and CKX enzyme activity were shown to be regulated by StCKXs. This study provides detailed information that can help future endeavors in the molecular breeding of potato (Solanum tuberosum).