The soldier, identified as non-commissioned officer Adrien Quélin, “died [on Tuesday] following an accident that occured during a maintenace operation in Timbuktu”, Defence Minister Florence Parly wrote on Twitter on Wednesday.
The government spokesperson, Gabriel Attal, told French TV an investigation was under way.
A total of 53 French soldiers have died in the restive Sahel region since Paris deployed a counter-terrorism force in 2013 to drive back militant groups that seized cities and towns in northern Mali.
A poor and landlocked nation, Mali continues to battle militant attacks and intercommunal violence, which often spill over to neighbouring countries.
France has begun re-organising its forces in the region this year, including by pulling out of its northernmost bases in Mali at Kidal, Timbuktu and Tessalit.
Total French troops in the region are to be cut from 5,000 today to between 2,500 and 3,000 by 2023.