The aim of this study was to determine the composition and content of phenolic compounds in extracts of plum fruit. Fruit of 17 plum cultivars were analyzed. Fruit samples were collected in 2019 from fruit trees with “Myrobalan” (P. cerasifera Ehrh.) and “Wangenheim Prune” (P. domestica L.) rootstocks. The following glycosides of the flavonol group were identified: avicularin, isorhamnetin-3-O-rutinoside, isoquercitrin, hyperoside, rutin, and an aglycone quercetin. Compounds of the flavan-3-ol group were identified, such as (+)-catechin, procyanidin C1, and procyanidin A2, along with chlorogenic acid attributed to phenolic acids and a non-phenolic cyclitol–quinic acid. Of all the analytes identified in plum fruit samples, quinic acid predominated, while chlorogenic acid predominated among all the identified phenolic compounds, and rutin predominated in the flavonol group. Hierarchical cluster analysis (HCA) and principal component analysis (PCA) revealed that fruit samples of “Kubanskaya Kometa”, “Zarechnaya Raniaya”, “Duke of Edinburgh”, “Jubileum”, and “Favorita del Sultano” cultivars had different quantitative content of phenolic compounds from that observed in other samples. The highest total amount of phenolic compounds was found in the European plum samples of the “Zarechnaya Rannyaya” cultivar, while the amount of quinic acid was the highest in plum fruit samples of the “Jubileum” cultivar.