"We were concerned to learn of the arrests of French journalist Jean-Philippe Remy and British photographer Philip Moore," Fabius said in a statement.
"I call on Burundi's authorities to proceed with their immediate release.
Diplomatic procedures are underway."
In a statement on its website, Le Monde demanded the release of both journalists, saying they were its special correspondents in Burundi.
The British Foreign Office said it was "urgently looking into reports" about the detention of a UK national.
Remy is the Africa bureau chief for the French newspaper Le Monde, while Moore, a freelance photographer, has often reported from conflict-prone countries in the region. Both men have won awards for their coverage of sub-Saharan Africa.
The two men were covering the crisis triggered in April last year by President Pierre Nkurunziza's decision to run for a controversial third term in office.
His quest to remain in power sparked weeks of street protests, a failed coup, frequent killings and a nascent rebellion.
The government has cracked down on the media, forcing independent outlets to shut down and driving some journalists into exile.
Remy has won several awards, including the 2013 Prix Bayeux-Calvados for his coverage of the war in Syria.
Moore, a freelance photographer, has frequently worked for AFP, Le Monde and other international publications, winning widespread acclaim for his photographs of conflicts in eastern Democratic Republic of Congo as well as Libya, Somalia and Syria.
Le Monde demanded the release of the two men, who it said were arrested on Thursday afternoon while meeting with government opponents.
French news service AFP’s chairman Emmanuel Hoog said the reporters "were arrested while carrying out their mission to inform" and demanded they "be released as soon as possible."
Hoog recalled that AFP's correspondent in Burundi, Esdras Ndikumana, who also worked for Radio France Internationale (RFI), was forced into exile after being arrested and beaten by government forces in August 2015.
Le Monde said Remy had entered the country on January 19, and Moore on January 21.
"Both had visas and were only doing their job by meeting all parties involved in the tensions in Burundi," said the paper.