Britain is due to leave the European Union on March 29, but has not yet reached a deal on a post-Brexit relationship, meaning companies with UK-issued licences may no longer have the right to provide some financial services in the EU.
The companies, a quarter of which hail from Britain, are looking to get electronic money institution licences, Marius Jurgilas, member of the board at the central bank, told Reuters in an interview.
"It seems that the companies, many of which are quite large, are behaving like a student who only starts worrying on the eve of an exam," he said.
He said Lithuania can process an electronic money institution licence application in as little as three months, compared to about a year in some EU countries, giving it an advantage over other fintech centres such as Luxembourg, Ireland or Belgium.
"It is an onslaught ... We do not have the resources to process all the applicants. We have to pick-and-choose, prioritising the least risky applicants," said Jurgilas, who did not provide names of the companies due to confidentiality rules.
Ireland's central bank said in October that it had seen a surge in financial services firms seeking to set up or extend their operations in Ireland as a result of Brexit and is processing over 100 applications.
Lithuania began attracting fintech companies a few years ago, and as of January has issued a total of 83 licences to such firms, second only to Britain among European Union countries, according to government figures.
The newcomers include a payment arm of Alphabet Inc's Google and Revolut, a British digital-only bank, and Jurgilas said the central bank is ready to step up its oversight capabilities as the sector grows.
Jurgilas dismissed suggestions that firms were drawn to Lithuania by a benign regulatory regime.
The "European Union has institutions which make sure that market supervisors in all its countries, including Lithuania, work to the same standard, and if any Lithuanian-registered bank grows into significant size, its supervision will be taken over by the European Central Bank", he said.
(This story changes headline, lead, third paragraph after Lithuania's central bank updated origin of the companies).
(Reporting By Andrius Sytas; Editing by Elaine Hardcastle)
By Andrius Sytas