Olivier Veran told Europe 1 radio that after arriving in France on Monday, the vaccine would be sent to cities with the highest virus circulation, from Strasbourg on the German border to Nice on the Mediterranean.
In addition to the continued distribution of Pfizer-BioNTech injections, Moderna doses would reach vaccination centers by Wednesday, Veran added.
The health ministry said in a statement that nearly eight million doses of the Moderna vaccine would arrive in France by July.
Like the Pfizer-BioNTech jab, it takes two injections spaced over several weeks for the Moderna version to achieve maximum effectiveness.
However, it poses fewer logistical problems as it only requires storage at -20 Celsius rather than around -80 C for the Pfizer-BioNTech vaccine.
After fiercely criticizing the government for a hesitant start to the campaign, Veran said that by the end of the weekend, more than 100,000 people had reportedly been vaccinated.
Neighboring Germany has already passed half a million, while Britain says it injects 200,000 a day.