Firms have recognized that the way upstream suppliers work with each other is important for their product innovation. However, it is still unclear what influences supplier–supplier (S-S) cooperation and competition in the supplier network have on their innovation. Thus, this study is aimed to take an ego network’s viewpoint to investigate the influence of horizontal S-S competition and cooperation in the supplier network on the ego buyer’s innovation, combining network theory with transaction cost theory and resource dependence theory. It takes the ego buyer’s supplier network as the analysis unit with cross-sectional data of 130 listed Japanese manufacturers and their supplier networks in 2016. The results of negative binomial regression indicate that both S-S competition and cooperation have inverted U-shaped effects on buyer innovation, although the result of S-S competition is not robust. It also shows S-S competition can play a moderating role in the relationship between S-S cooperation and buyer innovation. Regarding their interplay, simultaneously maintaining moderate cooperation and low competition among suppliers is the best choice for buyer innovation, whereas simultaneously maintaining high competition and cooperation among suppliers is also unexpectedly conducive for buyer innovation. This study contributes to linking the dyadic analysis of vertical relationships to the network analysis of horizontal S-S relations. It also provides insights to manufacturers on how to strategically manage horizontal S-S relations for their innovation.