Faye defeated the ruling coalition's candidate in a March election by a landslide, reflecting high hopes for change in the country of around 18 million.
The audit is one of the first policy moves announced since the 44-year-old former tax inspector's inauguration on Tuesday.
"The exploitation of our natural resources, which according to the constitution belong to the people, will receive particular attention from my government," he said.
"I will proceed with the disclosure of the effective ownership of extractive companies (and) with an audit of the mining, oil, and gas sector."
He did provide further details, but sought also to reassure investors, who he said were "welcome in Senegal."
"Investor rights will always be protected, as well as the interests of the state and the people," he said.
Senegal's first offshore oil development is due to start production in mid-2024. The Sangomar oil and gas project operated by Woodside Energy is expected to produce about 100,000 barrels per day.
(Reporting by Diadie Ba and Bate Felix; Writing by Alessandra Prentice; Editing by Chris Reese and Costas Pitas)
