Interior Ministry spokesman Najib Danish said the blast occurred at the entrance to a Kabul Bank branch, not far from the embassy.
There was no immediate claim of responsibility for the blast, which came as banks are busy with people withdrawing money ahead of the Muslim Eid holiday at the end of the week.
It was the latest explosion to rock the war-weary Afghan capital and comes a week after United States President Donald Trump committed American soldiers to Afghanistan indefinitely.
In May a massive truck bomb ripped through Kabul's diplomatic quarter, killing about 150 and wounding around 400 people, mostly civilians.