The Taliban claimed responsibility in a tweet for the attack in the centre in Gardez, capital of Paktia province which borders Pakistan.
“At first, a suicide bomber detonated a car filled with explosives near the training centre, making way for a number of attackers to start their assault,” the Afghan interior ministry said in a statement.
A local official said two car bombs blew up near the compound that also houses the provincial headquarters of the national police, border police and Afghan National Army.
Photos posted on Twitter purportedly show two large plumes of smoke rising above the city, suggesting two bombs were detonated in the assault.
Paktia borders Pakistan's tribal areas where the Taliban-affiliated Haqqani network has a presence.
The extremist group has been blamed for carrying out spectacular attacks across Afghanistan since the US-led invasion in 2001 and is known for its frequent use of suicide bombers.
It was blamed for the truck bomb deep in the heart of the Afghan capital Kabul in May that killed around 150 people.
The Haqqanis have also been accused of assassinating top Afghan officials and holding kidnapped Westerners for ransom.