Six government soldiers and about 20 rebels were wounded in the fighting, according to the ministry.
Mali's government says the Tuareg group is trying to control northern cross-border smuggling routes for arms and drugs.
The sides had agreed a Libyan-brokered ceasefire in April.
The calm collapsed when Tuareg fighters attacked a military supply convoy a month later. The Malian army had kept its troops on a war footing in the north, arguing that it did not trust the ceasefire would hold.
Mali's eastern neighbour Niger faces its own Tuareg-led revolt in which more than 70 soldiers have died in under a year, mainly in attacks near its northern uranium-mining zone.
Fiercely proud of their independence, the Tuareg nomads staged revolts in Mali in the 1960s and 1990s and in Niger in the 1990s seeking greater autonomy from black African-dominated governments.
Peace agreements after the 1990s rebellions aimed to grant Tuareg communities a greater degree of autonomy while at the same time integrating former fighters into the national army and promoting Tuareg politicians. But grievances have resurfaced.