The Financial Conduct Authority (FCA) said it had also banned Sonali Bank UK owned by the Bangladesh government from taking deposits from new customers for 168 days and has fined its former money laundering reporting officer, Steven Smith, £17,900.
Mr Smith has also been banned from taking on similar roles within regulated firms in the UK.
Sonali is the only UK-based Bangladeshi bank and had 85,625 customers registered to send money overseas in 2014.
It has around 2,500 customer accounts in Britain and offices in London, Birmingham and Bradford.
The FCA said Sonali failed to have proper anti-money laundering systems in place for nearly four years from August 2010 to July 2014, despite having been warned about weaknesses in its controls.
It said: “The FCA found serious and systemic weaknesses affected almost all levels of its anti-money laundering control and governance structure, including its senior management team, its money laundering reporting function, the oversight of its branches and its anti-money laundering policies and procedures.”
Blue Billywig Video PlayerThe watchdog added that it was also not informed by Sonali of an allegation of significant fraud while the bank was under investigation.
The FCA found that Mr Smith demonstrated a “serious lack of competence and capability” in his role, but said it took into account the fact he did not have the support of senior management and was overworked.
Mark Steward, director of enforcement and market oversight at the FCA, said: Fighting money laundering is an issue of extreme international importance and ensuring that anti-money laundering controls are effective and viewed as important throughout the business are fundamental obligations of all regulated firms.
“There is an abundance of guidance for firms on how to comply with anti-money laundering and financial crime requirements and no excuse for failing to follow it.”
The FCA said Sonali and Mr Smith saw their fines reduced by 30% for agreeing to settle early.
State-owned bank Sonali launched a UK arm in December 2001 to serve the ex-pat Bangladeshi community and previously had six branches in Britain.
Its turnover in 2014 was £10.1 million.
Simon Morris, a financial services partner with law firm CMS, said the penalty was a wake-up call to banks.
The FCA has imposed a very large fine for a very small bank to give off a clear signal that weaknesses in handling anti-money laundering responsibilities will not be tolerated, he said.