ABSTRACT Since the extreme value index (EVI) controls the tail behavior of the distribution function, the estimation of EVI is a very important topic in extreme value theory. Recent contributions have focused on nonparametric regression approaches with covariates for the estimation of EVI. However, for high‐dimensional settings, the fully nonparametric estimator faces the curse of dimensionality. To resolve this, we apply the single‐index model to EVI regression under a Pareto‐type tailed distribution. We study the penalized maximum likelihood estimation of the single‐index model. The asymptotic properties of the estimator are also developed. Numerical studies are presented to demonstrate the efficiency of the proposed model.