Just two soldiers are known to have survived unscathed after the attack on the base in the Chashmo area of Maiwand district in Kandahar province, the defence ministry said in a statement, adding that nine soldiers were wounded and six unaccounted for.
Defence ministry spokesman Dawlat Waziri told AFP the attackers detonated at least one explosive-packed Humvee vehicle and razed the compound in the early morning assault.
"We think the militants used an explosive-packed Humvee vehicle to detonate the gate of the base and we are looking to see if there was more than one," Waziri said.
"Unfortunately there is nothing left inside the camp. They have burned down everything they found inside."
The Taliban claimed the ambush in a message to journalists which said all 60 security personnel on the base were killed.
Ten insurgents died, the ministry said.
"We have sent a delegation to assess the situation. The base is under ANA (Afghan National Army) control," Waziri added.
In each assault the Taliban used a Humvee vehicle as a bomb to blast their way into their targets.
On Tuesday two attacks in southeast Afghanistan killed 80 people and wounded nearly 300 in the bloodiest day in the war-torn country in almost five months.
The deadliest of Tuesday's assaults was on a police compound in the city of Gardez in Paktia province where Taliban militants disguised as police detonated three explosive-packed vehicles -- including a truck and a Humvee -- that cleared the way for 11 gunmen to enter.
At least 60 people, including Paktia police chief Toryalai Abdyani and civilians waiting to collect documents, were killed in the blasts and ensuing battle that lasted around five hours, health officials said, with more than 230 wounded.
In the second attack in the neighbouring province of Ghazni, some 100 kilometres west of Gardez, 20 people, including 15 members of the security forces and five civilians died and 46 were wounded, officials said.