Police say Taliban security guards were one of those killed in the attacks that had not yet been charged.
The bombs killed at least five people and injured seven people in northeastern Afghanistan, local police report.
The explosion took place at 8:35am (04:05 GMT) on Tuesday near the Kabul Bank branch in Kunduz province. No group has yet to assert responsibility for the explosion.
Four other people, including bank security guards and members of civilians and Afghanistan’s dominant Taliban group, were among the people who were killed, police said.
“The suicide bombing, which improvised the explosive device, exploded itself,” said Junduz Police spokesman Jumadin Kaksal.
“Kunduz State Police Command will work with related organizations to find the perpetrators of the case and bring them to justice,” he added.
The number of bomb explosions and suicide attacks in Afghanistan has dropped significantly since the US withdrawal of its forces and the government it supported was expelled by the Taliban in August 2021.
However, many armed groups, including ISIL (ISIS), remain threats.
Dozens of people died in suicide bombings at the Siam Mosque in Kundus in October 2021, and ISIL affiliates in Korasan (ISKP) claimed responsibility.
Last March, suicide bombers killed at least three people when an attack claimed by the ISIL regional branch caused a bomb to explode outside a bank in southern Kandahar state.
Despite the ongoing attacks, Taliban authorities say they have almost crushed the group.
