This is the third suicide attack on army vehicles in two days, Xinhua reported citing a defence ministry spokesman.
"One suicide bomber detonated his explosive vest on an army bus in Doghabad locality in Dar-ul-Aman area, killing three army personnel and injuring 10 others," tweeted a defence ministry spokesman.
The bomber was also killed.
The Taliban insurgent group claimed responsibility for the attacks.
Zabiullah Mujahid, a purported Taliban spokesman, told local media from an undisclosed location that the targeted bus was carrying 30 Afghan army officers when it came under Taliban attack.
The bombing came two days after the country inked a security and defence agreement with the US.
On Wednesday morning, eight people, including seven army personnel, were killed and 21 others wounded when two suicide bombers targeted two army buses in western and northern Kabul.
The attacks also came three days after Ashraf Ghani Ahmadzai was sworn-in the new president of the war-torn country.
The Afghan army and police are taking up the responsibility of providing security for the country from the NATO-led troops. They are set to take the full responsibility by the end of the year.
More than 41,000 NATO-led coalition troops, down from the peak of 130,000 in 2010, are currently stationed in Afghanistan.
Nearly 29,000 of them are Americans and Washington plans to trim its forces down to less than 10,000 next year.