Social media influencers play a significant role in marketing by introducing products to their followers. We investigate how Instagram influencers impact consumer parasocial interaction (PSI) in the relationship between value perception and purchase intention. Whereas customers influence the attractiveness (social and physical) PSI of social media influencers, studies of the effects of luxury purchasing PSI in Thailand are limited. We examine the relationship between PSI and followers of luxury fashion’s value (social, personal, and conspicuous) on social media. We use structural equation modeling to evaluate hypotheses by conducting an online survey with 400 Thai millennial respondents who had experience following influencers on Instagram. The findings indicate that Thai millennials accept Instagram influencers’ PSIs in terms of value perception and motivation to purchase luxury fashion. The attractiveness of influencers initiates the formation of PSI; followers receive value perception and react to purchasing intention from influencers. The concepts were investigated to prove that influencers’ power can encourage followers to mitigate negative consequences by delivering value perceptions on PSI. These findings provided managerial implications for comprehending consumers in the field of digitalization.