Polycomb repressive complex (PRC) group proteins regulate various developmental processes in plants by repressing target genes via H3K27 trimethylation, and they function antagonistically with H3K4 trimethylation mediated by Trithorax group proteins. Tuberization in potato has been widely studied, but the role of histone modifications in this process is unknown. Recently, we showed that overexpression of StMSI1, a PRC2 member, alters the expression of tuberization genes in potato. As MSI1 lacks histone-modification activity, we hypothesized that this altered expression could be caused by another PRC2 member, StE(z)2, a potential H3K27 methyltransferase in potato. Here, we demonstrate that a short-day photoperiod influences StE(z)2 expression in the leaves and stolons. StE(z)2 overexpression alters plant architecture and reduces tuber yield, whereas its knockdown enhances yield. ChIP-sequencing using stolons induced by short-days indicated that several genes related to tuberization and phytohormones, such as StBEL5/11/29, StSWEET11B, StGA2OX1, and StPIN1 carry H3K4me3 or H3K27me3 marks and/or are StE(z)2 targets. Interestingly, we observed that another important tuberization gene, StSP6A, is targeted by StE(z)2 in leaves and that it has increased deposition of H3K27me3 under long-day (non-induced) conditions compared to short days. Overall, our results show that StE(z)2 and deposition of H3K27me3 and/or H3K4me3 marks might regulate the expression of key tuberization genes in potato.