The supply convoy was ambushed 18 km from the remote border garrison town of Tinzaouatene, which was briefly besieged in September by fighters led by Ibrahima Bahanga, the Malian Tuareg leader.
Authorities blame Bahanga's group for trying to control traditional Saharan smuggling routes between Algeria and Mali.
Mali has reinforced troops in the region after the attack, a military source told the AFP news agency.
The Tuaregs are also holding about 30 soldiers hostage, according to Malian military officials.
Colonel Abdoulaye Coulibaly, military spokesman, confirmed that several troops had been taken after a land mine attack on Thursday but refused to give details on how many were taken or the manner of their capture.
The reported hostage taking comes two weeks after the Tuaregs freed a group held since August.
Mali straddles the Sahara on a desolate expanse roamed by smugglers, rebel groups and nomads.
Last year, the rebels carried out raids and ambushes in parts of the Kidal region.
The Tuareg minority demand more autonomy and a greater share in their Saharan region's wealth, which includes deposits of uranium and gold.
However, the Niger and Malian governments dismiss them as bandits involved in trafficking arms and drugs.
The attack took place as Mali's government worked to help negotiators from Austria try to obtain the release of Andrea Kloiber, 43, and Wolfgang Ebner, 51, who went missing while on holiday in Tunisia last month.
Malian authorities have appealed to Tuareg community leaders in the Kidal region who might be able to act as mediators with the kidnappers of the Austrian hostages.
"Mali is going to let Austria freely negotiate the terms of release of the hostages ... offering its help where it's needed," a Malian official said.
Algerian-based al-Qaeda in the Islamic Maghreb says it seized the two tourists, while a Malian military source said they were being held in a hideout somewhere between the town of Kidal and the Algerian border.
In Vienna, Peter Launsky-Tieffenthal, Austria's foreign ministry spokesman, said Austrian authorities were doing their utmost to ensure the couple's safety.
The group has demanded a ransom and the release of 10 prisoners held in Algeria and Tunisia. It had set a deadline of midnight last Sunday for its demands to be met, but has extended this by a week.
There was no suggestion of any link between Thursday's attack and the kidnapping of the Austrians.