A review by the Financial Conduct Authority (FCA) found "serious weaknesses" in the procedures of the bank between December 2007 and July 2011.
The FCA said these were "particularly serious" because Standard, which has extensive operations in 18 African countries through its parent group, provided loans and other services to a significant number of corporate customers from countries where there was recognised to be a higher risk of money laundering.
"The weaknesses in Standard Bank's AML (anti-money laundering) systems and controls resulted in an unacceptable risk of Standard Bank being used to launder the proceeds of crime," the FCA said.
Tracey McDermott, director of enforcement and financial crime, said: "Banks are in the front line in the fight against money laundering.
"If they accept business from high-risk customers they must have effective controls and practices in place to manage that risk."
The failings related to the bank's dealings with companies linked to "politically exposed persons" (PEPs).
These are individuals who are, or have recently been "entrusted with a prominent public function" outside the UK, or their close relatives or associates. Guidance by the Financial Action Task Force, a global body, says many "are in positions that potentially can be abused for the purpose of committing money laundering offences" as well as corruption, bribery and terrorist financing.