"Starting on May 1st, the Zürcher Kantonalbank will cut all business relations with Cuba," the bank said on Tuesday in an email sent to AFP, confirming Swiss news reports.
"The bank is part of an international network and must respect international economic embargoes and restriction lists," it explained.
Bank spokeswoman Evelyne Brönnimann told AFP that new rules meant ZKB must now attest to its banking partners in the United States that its activities are in line with the US Office of Foreign Asset Control (OFAC) rules.
"If this is not the case, the United States can take actions against the banks like freezing their holdings," the bank statement said.
A number of international banks have been slapped with multi-million-dollar fines in the past year for flouting US sanctions on Cuba, as well for transactions with Iran, Libya, Myanmar and Sudan.
The bank said its decision would impact 12 clients, but did not provide details on who they were.
The head of the Swiss-Cuban Chamber of Commerce, Andreas Winkler, however, told AFP the move would especially affect small and medium-sized Swiss companies and non-governmental organisations (NGOs) that dealt with Cuba.
Winkler harshly criticised ZKB's decision, lamenting that the bank was removing the only banking channel operating in Swiss francs.
"Now operations will need to go through European banks that operate in euros," he said, pointing out that the extra exchange process would end up costing businesses more money.
He also questioned whether ZKB was actually required to cut business ties with Cuba under the OFAC rules, since it is not a US bank, or whether it was just playing it safe.
Washington has faced international criticism since it imposed its embargo on Cuba more than five decades ago.