The purpose of this article is to investigate whether the wide scope of supply chain collaboration including both customers and suppliers (Upstream–downstream External Collaboration) determines the greening of innovation more significantly than the scope limited only to suppliers (Upstream External Collaboration) or customers (Downstream External Collaboration). This goal was achieved as part of extensive research on the impact of relational capital on the innovativeness of high-tech companies in Poland. The results of the research were analysed using fuzzy conversion scales and descriptive statistics based on triangular fuzzy numbers. The application of the achievements of the fuzzy sets theory made it possible to test the hypotheses presented in the article with the use of fuzzy analysis of variance (fuzzy ANOVA). The findings confirm that the subjective scope of collaboration in the supply chain is important for greening innovation. Companies that cooperate with both suppliers and customers (Upstream–downstream External Collaboration) declared a greater tendency to green their innovations than those that cooperate with only one group of partners. The research findings contribute to the literature on the role of collaboration in the ecological responsibility and environmental performance of supply chain partners. The conclusions may have practical implications for the design and implementation of strategies in sustainable supply chain management. The study provides important lessons for SC managers facing the challenge of sustainable management during and after the COVID-19 outbreak.