It is well noted in the literature that volatility responds differently to positive and negative shocks. In this paper, we explore the impact of ESG ratings on such asymmetric behavior of volatility. For this analysis, we use the return data, ESG ratings, and solvency ratios of the constituent stocks of S&P Europe 350 for the period January 2016–December 2021. We apply autoregressive moving average models for the conditional means and GARCH and stochastic volatility models for the conditional variances to estimate the asymmetry coefficients. Afterwards, these coefficients are regressed via Arellano–Bond and lagged first difference methods to estimate the impact of ESG ratings. Our findings confirm that stocks of riskier firms are more likely to suffer from asymmetry behavior of volatility. We also confirm that firm leverage is linked to this asymmetry behavior. We found evidence that the impact of ESG ratings was negative before COVID-19, but positive afterwards. For some sectors, higher ESG ratings are linked to higher asymmetry. Finally, we found that during COVID-19, the asymmetry behavior became more pronounced.