Invasive alien species (IAS) constitute a major threat to global biological diversity. In order to control their spread, a detailed understanding of the factors influencing their distribution is essential. Although international trade is regarded as a major force structuring spatial patterns of IAS, the role of other social factors remains unclear. Despite studies highlighting the importance of strong governance in slowing drivers of biodiversity loss such as logging, deforestation, and agricultural intensification, no study has yet analyzed its contribution to the issue of IAS. Using estimates of governance quality and comprehensive spatiotemporal IAS data, we performed multiple linear regressions to investigate the effect of governance quality upon the distribution of species listed under “100 of the worst” IAS in 38 Eurasian countries as defined by DASIE. Our model suggested that for countries with higher GDP, stronger governance was associated with a greater number of the worst IAS; in contrast, for the lowest GDP countries under analysis, stronger governance was associated with fewer of these IAS. We elucidate how the quality of governance within a country has implications for trade, tourism, transport, legislation, and economic development, all of which influence the spread of IAS. While our findings support the common assumption that strengthening governance benefits conservation interventions in countries of smaller economy, we find that this effect is not universal. Stronger governance alone cannot adequately address the problem of IAS, and targeted action is required in relatively high-GDP countries in order to stem the influx of IAS associated with high volumes of trade.