The Cuban government says it will not be able to renew passports and process visas unless it finds an alternative to the M&T bank.
The M&T bank said its decision was taken for business reasons.
The move is likely to prevent tens of thousands of people travelling from the US to Cuba every month and could have a big impact on the economy there.
The US broke off diplomatic relations with Cuba in 1961 and imposed an economic embargo a year later.
In the absence of bilateral contacts, consular services have been handled by the Cuban Interests Section in Washington.
In a statement, the Cuban government blames the trade embargo for its failure to find a new bank “in spite of huge efforts made”.
The M&T bank announced last year that it would stop accepting deposits from February 17, which is a public holiday in the US.
“The section regrets any inconvenience this situation may cause,” read the statement.
The bank says it will only be able to handle “humanitarian cases”.
More than 40,000 people on average travel to Cuba from the US every month, most of them Cuban-Americans, according to the Miami-based Havana Consulting Group.
Americans who do not have Cuban nationality are also allowed to travel if they are taking part in cultural exchange programs.
Cuba and the US announced the resumption of official talks on immigration and postal services between the two countries.
Earlier this week, the EU agreed to open negotiations aimed at restoring full relations with Cuba.
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