Fragmentation and vegetative regeneration from small fragments may contribute to population expansion, dispersal and establishment of new populations of introduced plants. However, no study has systematically tested whether a high capacity of vegetative regeneration is associated with a high degree of invasiveness. For small single-node fragments, the presence of internodes may increase regeneration capacity because internodes may store carbohydrates and proteins that can be used for regeneration. We conducted an experiment with 39 stoloniferous plant species to examine the regeneration capacity of small, single-node fragments with or without attached stolon internodes. We asked (1) whether the presence of stolon internodes increases regeneration from single-node fragments, (2) whether regeneration capacity differs between native and introduced species in China, and (3) whether regeneration capacity is positively associated with plant invasiveness at a regional scale (within China) and at a global scale. Most species could regenerate from single-node fragments, and the presence of internodes increased regeneration rate and subsequent growth and/or asexual reproduction. Regeneration capacity varied greatly among species, but showed no relationship to invasiveness, either in China or globally. High regeneration capacity from small fragments may contribute to performance of clonal plants in general, but it does not appear to explain differences in invasiveness among stoloniferous clonal species.