The money was withdrawn in less than three hours from 1,400 convenience store cash machines across Japan, the Kyodo news agency reports.
The withdrawals targeted 7-Eleven cash machines, which unlike most in Japan accept foreign cards.
South Africa’s Standard Bank estimated its total losses at $19.25m.
Police suspect more than 100 people were involved across Japan, Kyodo said, putting the date of the incident as 15 May.
The maximum amount of 100,000 yen ($913; £629) was withdrawn in each of 14,000 transactions, said the agency, citing “investigative sources”.
Standard Bank described the heist as “a sophisticated, co-ordinated fraud incident” involving what it said was a “small number” of fake cards from account data belonging to it.
But it said customers had not suffered any losses themselves.
“Standard Bank has taken swift action to contain the matter” it said in a statement.
Japanese police are now examining security camera footage to identify suspects, and both countries are working with world police body Interpol to investigate how the data was stolen and how the heist was co-ordinated.
So far, no-one is reported to have been arrested in connection with the incident.
Source: BBC News