For more than two decades now, current-account imbalances are a crucial issue in the international policy debate as they threaten the stability of the world economy. More recently, the government debt crisis of the European Union shows that internal current account imbalances inside a currency union may also add to these risks. Oil price fluctuations and a contracting monetary policy that reacts on oil prices, previously discussed to affect the current account may also be a threat to the currency union by changing internal imbalances. Therefore, in this paper, we analyze the impact of oil price shocks on current account imbalances within a currency union. Differences in institutions, especially labor market institutions and trade result in an asymmetric reaction to an otherwise symmetric shock. In this context, we show that oil price shocks can have a long-lasting impact on internal balances, as the exchange rate adjustment mechanism is not available. The common monetary policy authority, however, can reduce such effects by specifying an optimum monetary policy target. Nevertheless, we also show that there is no single best solution. CPI, core CPI or an asymmetric CPI target all come at a cost either regarding an increase in unemployment or increasing imbalances.