At least one woman was killed and 19 others wounded in the powerful blast, which left the Roshan Telecom bus badly mangled and the area littered with smouldering debris and twisted metal.
No group has so far claimed responsibility for the assault, but it comes as the Taliban step up attacks even before the official start of the annual spring offensive.
"Kabul Police have arrested three suspects related to an explosion in which 19 civilians, including four women, were wounded and one woman was killed," interior ministry spokesman Sediq Sediqqi said on Twitter.
Security officials cordoned off the area as firefighters and ambulances rushed to the scene as clouds of smoke filled the air.
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The bombing comes after gunmen disguised as doctors stormed Sardar Daud Khan hospital in Kabul last Wednesday, with insiders including two interns among the attackers, multiple surviving staff and security sources told AFP.
The defence ministry insists only around 30 people were killed by five attackers. But security sources and the survivors, some of whom counted dead bodies, said the death toll exceeded 100.
The savagery of the assault was characterised by how the assailants stabbed bed-ridden patients, threw grenades into crowded wards and shot people from point-blank range.
The Islamic State group claimed it was behind the attack via its propaganda agency Amaq -- hours after the Taliban denied responsibility.
But the survivors AFP spoke to said the attackers chanted "Allahu Akbar" (God is great) and "Long live Taliban" in Pashto.
The Afghan defence ministry said a government commission had been set up to investigate the attack.
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