MILAN—Britain’s vote to leave the EU has produced dire predictions for the U.K. economy. The damage to the rest of Europe could be more immediate and potentially more serious. Nowhere is the risk concentrated more heavily than in the Italian banking sector.

In Italy, 17% of banks’ loans are sour. That is nearly 10 times the level in the U.S., where, even at the worst of the 2008-09 financial crisis, it was only 5%. Among publicly traded banks in the eurozone, Italian lenders account for nearly half of total bad loans.

Years of lax lending standards left Italian banks ill-prepared when an economic slump sent bankruptcies soaring a few years ago. At one major bank, Banca Monte dei Paschi di Siena SpA, bad loans were so thick it assigned a team of 700 to deal with them and created a new unit to house them. Several weeks ago, the bank put the bad-credit unit up for sale, hoping a foreign partner would speed the liquidation process.

The U.K. vote to exit the European Union has compounded the strains on Europe’s banks in general and Italy’s in particular. It imperils the Monte dei Paschi sale, some bankers say, and creates fresh uncertainty at a time when lenders are struggling with ultralow and even negative interest rates and sluggish economic growth.

Brexit has many executives concerned that central banks will keep interest rates lower for longer than they might otherwise, in an attempt to counteract the slower growth—in the eurozone as well as Britain. European banks’ stocks slid after the vote, with those in Italy especially hurt. Shares in Monte dei Paschi are down roughly a third since the June 23 referendum.