Macri's chief of staff Marcos Pena and Finance Minister Alfonso Prat-Gay are also targeted in the investigation, prosecutors said.
It was opened by a prosecutor after a leftist lawmaker accused the center-right president of abuse of office and violating regulations on public officials.
The controversy stems from a November decree that tweaked an earlier law granting amnesty to Argentines who repatriate undeclared assets from overseas.
Public officials and their families were initially excluded from the amnesty, which Congress passed in July.
But under the decree -- signed by Macri, Pena and Prat-Gay -- officials' spouses, parents and children can now take part if the assets in question were acquired before their relative took office.
Outraged, the opposition accused Macri of trying to protect his father, the Italian-born business magnate Franco Macri, who is known to have overseas assets.
Macri and his father were both named in the Panama Papers scandal, which revealed their offshore dealings in tax havens such as the Bahamas.
Holding undeclared assets overseas is common practice in Argentina, a country with a history of hyperinflation and other economic crises.
The amnesty law ostensibly aims to bring that money home to boost investment in the sputtering economy.
So far, Argentines have declared nearly $7 billion in unreported cash and $20 billion in overseas assets under the program, according to official figures.