This study develops cluster robust inference methods for panel quantile regression (QR) models with individual fixed effects, allowing for temporal correlation within each individual. The conventional QR standard errors can seriously underestimate the uncertainty of estimators and, therefore, overestimate the significance of effects, when outcomes are serially correlated. Thus, we propose a clustered covariance matrix (CCM) estimator to solve this problem. The CCM estimator is an extension of the heteroskedasticity and autocorrelation consistent covariance matrix estimator for QR models with fixed effects. The autocovariance element in the CCM estimator can be substantially biased, due to the incidental parameter problem. Thus, we develop a bias‐correction method for the CCM estimator. We derive an optimal bandwidth formula that minimizes the asymptotic mean squared errors, and propose a data‐driven bandwidth selection rule. We also propose two cluster robust tests, and establish their asymptotic properties. We then illustrate the practical usefulness of the proposed methods using an empirical application.