Exploring the effect of an economic crisis on the carbon market can be propitious to understand the formation mechanisms of carbon pricing, and prompt the healthy development of the carbon market. Through the ensemble empirical mode decomposition (EEMD), a multiscale event analysis approach is proposed for exploring the effect of an economic crisis on the European carbon market. Firstly, we determine the appropriate carbon price data of the estimation and event windows to embody the impact of the interested economic crisis on carbon market. Secondly, we use the EEMD to decompose the carbon price into simple modes. Hilbert spectra are adopted to identify the main mode, which is then used to estimate the strength of an extreme event on the carbon price. Thirdly, we perform a multiscale analysis that the composition of the low-frequency modes and residue is identifying as the main mode to capture the strength of the interested economic crisis on the carbon market, and the high-frequency modes are identifying as the normal market fluctuations with a little short-term effect on the carbon market. Finally, taking the 2007–2009 global financial crisis and 2009–2013 European debt crisis as two cases, the empirical results show that contrasted with the traditional intervention analysis and event analysis with the principle of “one divides into two”, the proposed method can capture the influences of an economic crisis on the carbon market at various timescales in a nonlinear framework.