The objective of this article is to analyse how the Single Supervision Mechanism (SSM), the first pillar of the European Banking Union, affects contagion between bank and sovereign risk in the eurozone. Additionally, we test whether this contagion is transmitted from banks to sovereigns or vice versa, and how this transmission differs before and after the SSM. On the one hand, using quarterly data from 80 banks and 13 eurozone countries over the period 2009-2016 (2,441 observations), we do not find solid evidence that the SSM reduces contagion from sovereign risk to banks' stock returns. On the other hand, the analysis of credit default swap (CDS) spreads comprises quarterly data from 25 banks and 10 eurozone countries between 2009 and 2016 (771 observations). We find that the announcement of the SSM in March 2013 reduces contagion between bank and sovereign CDS spreads. Additionally, before the announcement of the SSM, an increase in sovereign risk does not alter contagion. However, after this announcement, an increase in sovereign risk leads to lower contagion. Therefore, the announcement of the SSM has an immediate effect on CDS spreads, while there is not enough evidence for banks' stock returns.