Background/Objectives: Sosnowsky’s hogweed Heracleum sosnowskyi, which originated in the Greater Caucasus region and spread rapidly across Central and Eastern Europe after being introduced as cattle fodder in the 1950s, is an example of an extremely dangerous invasive species listed by the European Union. This study aimed to estimate the genetic diversity of 6 native populations of Sosnowsky’s hogweed from the Caucasus region of Russia and Georgia, as well as 15 invasive populations from Lithuania and Poland, and to assess the adaptability of hogweed in new environments. Methods: Genetic analyses of plant material were conducted, including DNA extraction, ISSR genotyping, PCR product separation, and subsequent molecular data mining and analysis. Results: A pairwise Mantel test revealed a positive correlation between geographical distance and the genetic diversity of the hogweed populations. The presence of three distinct allele pools was confirmed in the populations under study, with genotypes from Poland dominated by the first allele pool, which had the largest number of polymorphic and private loci. Analysis of molecular variance by origin showed that 99% of the variation was within the analysed hogweed populations, with only 1% being between them. Native populations from Russia were genetically distinct from those in Poland and Lithuania. Some of the Georgian population shows genetic similarities to Russians, while the rest shows similarities to the secondary invasive Lithuanians. Conclusions: Introduced populations of H. sosnowskyi are characterised by considerable genetic variation, likely resulting from multiple introductions and subsequent evolutionary processes, which may facilitate local adaptation and invasiveness, although overall large-scale genetic differentiation remains low.