Background: A recent study in Nature Climate Change shows that due to reduced human activities during the Coronavirus disease 2019 (COVID-19) pandemics, daily global emissions of carbon dioxide decreased by 17% from the average level in 2019. With the gradual recovery of economic activity and human energy consumption, the emissions of greenhouse gas and pollution would rise again. Green bonds are considered a crucial tool to release climate finance. The green bond market can act as an essential bridge between capital providers (i.e. institutional investors) and sustainable assets (i.e. renewable energy).This study is the first attempt to examine co-movement and the lead–lag relationship between green bonds and global and sector renewable energy stock markets in the time and frequency horizons. We apply continuous wavelet, wavelet coherence, and line and non-line causality approaches on data during the period 2010–2020, coincidentally including the COVID-19 pandemic.Results: (1) Green bonds and renewable energy markets show evidence of a similar pattern based on the wavelet power spectrum, which shows high price volatility at small and medium scales, especially during periods of turbulence and crisis. (2) The dynamic connection between green bonds and renewable energy returns is weak (strong) on the short (long) time-scale. However, on medium-term time scales, the dependence between them is significant only during turbulent periods, such as the European Sovereign Debt Crisis 2012 (ESDC) and the COVID-19 pandemic. (3) With regard to causality, our results show unidirectional and bidirectional linear (non-linear) causality at low and high frequencies. Moreover, our finding reveals the fact regarding the lead–lag relationship that, most of the time and frequencies, no one market necessarily dominates the other.Conclusion: Our findings provide several remarkable policies and practical implications for market regulators and investors. Institutional investors can benefit by including green bonds in their portfolios to decrease their climate change risk and improve their environmental, social, and corporate governance rating in the portfolio. Considering that the dependence between green bonds and renewable energy stock prices varies over various time scales, investors with different investment horizons should make diverse investment portfolio and hedging choices. The finding is also relevant for formulating green finance policies and supporting renewable energy investments. Policy decisions on the transition of energy to a decarbonized economy should consider the consequences for green bonds, which are also critical for the transition to a climate-resilient economy.