Two other French soldiers were injured in the "violent clash" overnight in the Tigharghar mountain range, Defence Minister Jean-Yves Le Drian said yesterday.
The killed soldier was a 32-year-old former Afghanistan veteran who belonged to Commando Parachute Group 10.
"Our troops approached a terrorist camp of around 30 individuals. Particularly violent clashes then took place that (Tuesday) night," Le Drian said in a statement.
Hollande "expresses his deep respect for the sacrifice" of the officer during "a particularly perilous mission", the Elysee Palace said in a statement.
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French troops intervened in Mali in January 2013 to chase out hardline Islamists, including Al-Qaeda in the Islamic Maghreb, which had seized control of the country's northern desert cities.
This intervention was replaced several months ago by a wider counter-terrorism operation, codenamed Barkhane, in five countries along the southern rim of the Sahara including Mali.
The operation is currently focusing on stemming a resurgence of jihadists in Mali and cutting their rear bases in Libya.