A US judge froze the assets of Sir Allen and the other defendants as well as those of the Stanford Group, its Antigua-based subsidiary Stanford International Bank (SIB) and another subsidiary, investment advisor Stanford Capital Management.
The Bank of Antigua is part of Sir Allen's global business interests but is separate from SIB.
A finance ministry official told Antiguan radio: "Your savings are safe. Do not panic."
At one branch in the Antigua capital St John's about 600 people queued, Reuters news agency said. A similar-sized crowd was seen at another branch near the airport.
Queues of customers formed outside Bank of Antigua branches
Prime Minister Baldwin Spencer said on Tuesday that the charges against Sir Allen could have "catastrophic" consequences for the nation, but he also urged people not to panic.
The Stanford group is the largest private employer in Antigua and Barbuda, covering financial, media and sporting franchises.
In Colombia, the local arm of the Stanford Group stopped trading on the stock exchange.
The SEC said on Tuesday that the fraud was "based on false promises and fabricated historical return data".
The England and Wales Cricket Board (ECB) suspended sponsorship negotiations with Sir Allen following the fraud charges.
The Stanford Group says it is worth more than $40bn, and Forbes magazine lists Sir Allen as the world's 605th richest man.
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