But deposits in the bank will be protected, as will investors in so-called senior bonds.
The banks will continue to operate and depositors will not suffer any inconvenience, officials said.
The action is likely to raise questions about Monte dei Paschi di Siena, an Italian bank that suffers from some of the same problems as the two banks that failed but is much larger. The Italian government has established a 20 billion euro (about $22.4 billion) fund to supply capital to Monte dei Paschi and other troubled Italian banks.
All Italian banks are plagued by bad loans and slack demand for credit because of the country’s stagnant economy. But Veneto Banca and Banca Popolare di Vicenza are the first Italian banks to be declared effectively dead by the European Central Bank and wound down.
The central bank said Friday that it had been keeping a close eye on Veneto Banca and Banca Popolare di Vicenza since 2014, when it was clear that both were short of capital. After the condition of both banks continued to deteriorate, the central bank asked the lenders to explain how they would rebuild their capital buffers.
“Both banks presented business plans which were deemed not to be credible by the E.C.B.,” the central bank said Friday in a statement.
Intesa Sanpaolo, Italy’s second-large bank after UniCredit, said earlier this week that it would be interested in buying the healthy parts of Veneto Banca and Banca Popolare di Vicenza. The bad loans and other troubled assets will be put into a separate “bad bank” and probably sold at a deep discount.
By announcing the failure of the banks on a Friday evening, the European Central Bank gave financial markets the weekend to absorb the news, in hopes that the news would not cause turmoil. Financial markets reacted calmly to the collapse of Banco Popular earlier in June, a sign that the eurozone’s system for troubled banks was working.
In Italy, protecting small investors in troubled banks has been a sensitive political issue, with elections expected by next spring. The protection of the senior bondholders of Veneto Banca and Banca Popolare di Vicenza may ease pressure on the Italian government.