Local media cited unconfirmed reports that the target was a guesthouse frequented by foreigners near the Spanish embassy in the city’s affluent Sherpur area.
No group has so far claimed responsibility for the attack, which comes as the resurgent Taliban escalate attacks against government and foreign targets.
“A car bomb hit Sherpur but the exact target is not immediately clear,” said CID chief Fraidoon Obaidi.
“The attackers are firing gunshots, it’s very dark and we are trying to be cautious.”
Sherpur is home to several foreign NGOs and residences of senior government officials, including former warlord Abdul Rashid Dostum, Afghanistan’s first vice-president.
“Initial reports of the explosion; car explosion in the vicinity of Shir Pur area of Kabul, we are working on more details,” tweeted interior ministry spokesman Sediq Sediqqi.
Security officials cordoned off the streets and ambulances with wailing sirens were seen rushing to the scene.
The attack follows a 27-hour Taliban siege this week of Kandahar airport, the largest military installation in southern Afghanistan, in which at least 50 people died, including women and children.
Eleven suicide attackers on Tuesday breached the high-security complex which also houses a joint NATO-Afghan base, taking families hostage and triggering pitched firefights with soldiers.
As the country grappled with the aftermath of the attack, its spy chief on Thursday quit his post, laying bare disagreements with President Ashraf Ghani over his diplomatic outreach to Pakistan.
The resignation of Rahmatullah Nabil on Thursday highlights the domestic backlash Ghani faces over his attempts to repair strained relations with Islamabad, long blamed for nurturing the Taliban.
But Ghani has staked considerable political capital in advocating bonhomie with the neighbour, saying it was a necessary partner in restarting peace talks aimed at ending Afghanistan’s long war.