It was not immediately clear if the explosion was a bomb.
The blast hit "an international contractor company's car", interior ministry spokesman Najib Danish told AFP, adding that the four wounded were all civilians.
Local media showed images of damage to houses and shops in the area.
If confirmed as an attack, it would be the latest to hit Kabul, which is one of the deadliest places in Afghanistan for civilians as both the Taliban and the expanding Islamic State group step up their assaults on the city.
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Ghani revealed his plans in a speech during international peace talks in Kabul this week that went better than expected, with officials in Washington daring to hold out hope that the longest war in its history may be heading to a negotiated settlement.
But Kabul remains on high alert, fearing further violence.
Since mid-January, militants have stormed a luxury hotel, bombed a crowded street, raided a military compound and launched a suicide attack during morning rush hour in the capital, killing more than 130 people.