Hamza Waziristani was killed in an air strike overnight in the eastern province of Ghazni where the bomber struck an Afghan military base on Sunday.
"The mastermind behind yesterday's terrorist attack on the (Ghazni) base was killed along with seven other terrorists," the defence ministry said in a statement.
Military spokesman Fawad Aman told AFP that the bomber was a Taliban militant from the Pakistani border region of Waziristan.
The attack was one of the deadliest in months targeting government forces in Afghanistan, where violence has surged since the start of peace talks between President Ashraf Ghani's administration and the Taliban in Qatar.
No group has claimed the attack.
The Taliban often do not comment on deadly attacks they are accused of carrying out.
The insurgents have launched near daily attacks against Afghan forces, primarily in rural areas, since signing a deal with Washington in February that paved the way for the withdrawal of foreign troops by May 2021.
Health officials in Ghazni said 30 people died in Sunday's attack, but the defence ministry - which is known to downplay tolls in attacks against its forces - said 10 were killed.
Violence has also surged in Kabul in recent weeks, with more than 50 people killed in two assaults on educational centres and a rocket attack.
The three Kabul attacks were claimed by the Islamic State group, but Afghan officials blamed the Taliban - who denied any involvement.
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