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4 year oldThe investigation focuses on three senior figures, including outgoing Prime Minister Edouard Philippe, following complaints from unions and doctors.
Earlier on Friday, Mr Philippe resigned amid a cabinet reshuffle.
The government has faced criticism over shortages of medical equipment during the pandemic.
Hours after Mr Philippe's resignation, it was announced that the Law Court of the Republic, which deals with claims of ministerial misconduct, would open an inquiry into the way his government handled the pandemic.
Along with the outgoing prime minister, those under investigation include Agnès Buzyn, who stepped down as health minister in February, and her successor Olivier Véran, senior public prosecutor François Molin said.
France has reported 202,673 confirmed cases of Covid-19 and 29,875 deaths.
Mr Macron came to power three years ago but now faces an economic crisis after the coronavirus pandemic.
A reshuffle has been expected for some time, however, and it is common practice for a French president to replace a prime minister during the five-year term in office known as the "quinquennat".
Mr Philippe's future as prime minister had been in doubt for several weeks and he will now take up the post of mayor in Le Havre, after winning the local vote on Sunday.
"For three years he's been by my side... we've carried out important, historic reform often in very difficult circumstances. We have a relationship of trust that's in a way unique in terms of the French Republic," the president said of Mr Philippe in a newspaper interview.
Jean Castex, 55, is little known in France, but he is a senior civil servant and has played a key role in the government's response to the Covid-19 pandemic.
He received the nickname "Mr Déconfinement", after Mr Philippe chose the Republicans party mayor from Prades in the Pyrenees to co-ordinate France's strategy of lifting the lockdown.
He attended the same elite university as Mr Macron and Mr Philippe and, like Mr Philippe, was previously a member of the right-wing Republicans party.
On Friday evening, Mr Castex warned in a speech that "the health crisis is, unfortunately, not over" and that "the economic and social crisis is already here".
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