The attack began when a suicide bomber drove an explosives-laden American-made Humvee armoured vehicle, likely captured from Afghan security forces, into the gate of the base, an army official told Reuters.
In a statement, the Ministry of External Affairs stated that "We strongly condemn the barbaric attack at the Afghan National Army base in Kandahar province".
Nine other militants were killed alongside him in the drone strike, the group's spokesman said.
The Afghan Defencee Ministry confirmed that at least 43 people had died.
Militants launched two separate attacks on Afghan security installations killing dozens of soldiers Thursday, the latest in a series of devastating assaults this week that left more than 120 people dead and underscored spiralling insecurity.
Separately Thursday, militants besieged a police headquarters in the southeastern province of Ghazni, attacking it for the second time this week.
It was the third suicide and gun attack on a security installation this week and takes the total death toll to more than 100, including soldiers, police and civilians.
Still, Nicholson continued to describe the fight in Afghanistan, America's longest-running war, as a stalemate.
The Western-backed government in Kabul is struggling to beat back insurgents in the wake of the exit of most North Atlantic Treaty Organisation forces in 2014.
And the base itself sustained major damage.
"After the explosion, we heard shootings, and then more explosions".
On October 17, at least 20 people were killed and several injured after suicide attackers and gunmen stormed a police training centre in southeastern Afghanistan. The battle ended with a US airstrike that killed nine Taliban fighters, North Atlantic Treaty Organisation officials said.