The watchdog organisation said its letter to Gigaba was also sent to Yunus Carrim, chairperson of Parliament’s standing committee on finance.
"Gigaba is responsible for determining the date on which the legislation must commence, but Corruption Watch is concerned that sufficient measures might not have been put into place in order for the legislation to become effective before the next review of the Financial Action Task Force (FATF), and whether these deficiencies will result in South Africa failing to meets its FATF obligations," the organisation said on Monday.
"The FATF holds its next plenary session from 21 to 23 June and had delayed making a public statement on South Africa’s Fica progress until after that meeting."
The FATF monitors country members' compliance with anti-terrorism and anti-money laundering regulations.
The bill was finally signed into law by President Jacob Zuma in April after he had sent it back to the National Assembly over concerns regarding searches without warrants.
The law provided for ongoing monitoring of the business relationships, sources of wealth and sources of funds of domestic prominent influential persons, their family members and close associates.
The DA had previously raised its concerns with the implementation of the law, alleging that Gigaba may delay such implementation because of Zuma's close ties to the controversial Gupta family.
"What this means is that President Jacob Zuma and his most important clients, the Guptas, are going to feel the heat as their business relationships, sources of wealth, and sources of funds are subjected to ongoing monitoring by financial institutions in South Africa," DA spokesperson David Maynier said two months ago.
Gigaba has featured in the leaked #GuptaEmails that showed that he allegedly took decisions that benefited the Guptas while he was public enterprises minister and later minister of home affairs.
He denied the allegations last week, adding that he did nothing wrong in the execution of his ministerial duties.
The law would only take effect after a date is determined by finance minister and published in the Government Gazette.