She has been accused of using a bank card provided by a charity to make personal purchases worth tens of thousands of dollars.
She is to step down after ceremonies to mark the 50th anniversary of the island's independence next week.
Denying wrongdoing, she said she had refunded all the money, Reuters news agency reports.
Ms Gurib-Fakim is a renowned scientist and in 2015 became the first woman to be appointed to the ceremonial position of president of Mauritius.
"The president of the republic told me that she would resign from office and we agreed on the date of her departure," Prime Minister Pravind Jugnauth told reporters without giving the chosen date.
"The interest of the country comes first, and I am proud of Mauritius's image as a model of living democracy in the world."
He added it would take place before parliament returned at the end of the month.
The Mauritian daily L'Express published bank documents purporting to show Ms Gurib-Fakim had used a credit card given to her by the Planet Earth Institute (PEI) in London to buy thousands of dollars worth of clothes, jewellery and other personal items.
According to the paper, the card was given to her as part of her work as an unpaid director for the charity.
One of the organisation's directors is Angolan businessman Alvaro Sobrinho who, the paper says, secured a permit to found an investment bank in Mauritius, prompting allegations of favouritism.
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