BRUSSELS—The European Commission on Sunday authorized Italy to use government guarantees to provide liquidity support to its banks, a spokeswoman said, disclosing the first intervention by a European Union government into its banking system following the U.K. vote to leave the EU.

The June 23 referendum sparked a steep sell-off in banking stocks followed by intense volatility this week. That has exacerbated already existing troubles in the Italian banking sector, which is suffering from high levels of bad loans and poor profitability...