The bomber, who was riding a motorcycle, set off the blast near the main market in the Afghan capital.
Ali Shah Paktiawal, a police official in Kabul, said the attack took place at approximately 8 a.m. local time "in Asmayee Wat in front of Nabawi Mosque."
Police said the bomber was apparently targeting a top intelligence official, who was among the wounded.
"The attacker has died and the investigation is continuing," Paktiawal said.
Mullah Dadullah, the main Taliban military commander in Afghanistan, claimed responsibility for the attack.
Taliban insurgents have stepped up attacks in recent weeks, but much of the violence has been focused in Afghanistan's south.
Authorities said today they were searching for four Health Ministry staff kidnapped by gunmen in the southern province of Kandahar on March 27.
(AFP, Reuters)
The Afghan Insurgency
HOMEGROWN OR IMPORTED? As attacks against Afghan and international forces continue relentlessly, RFE/RL hosted a briefing to discuss the nature of the Afghan insurgency. The discussion featured Marvin Weinbaum, professor emeritus of political science at the University of Illinois at Urbana-Champaign, and RFE/RL Afghanistan analyst Amin Tarzi.
LISTEN
Listen to the entire briefing (about 83 minutes):