The blast, in the west of the city during the morning rush hour, sent a huge cloud of gray smoke billowing into the sky.
The Taliban said a “recruitment center” had been attacked by one of their suicide bombers.
“A large number of soldiers and police were killed or wounded,” the Taliban said in a statement.
Government security officials said they were searching the scene and expected to update casualty details later.
The bomb went off when a vehicle was stopped at a checkpoint outside the police station, said interior ministry spokesman Nasrat Rahimi.
A health ministry spokesman said 95 wounded people had been taken to hospitals. Most of them were civilians, including women and children, he said.
“Again a Taliban suicide attack in Kabul targets a civilian area that resulted in harming of so many innocents,” Sediq Sediqqi, a spokesman for President Ashraf Ghani, said on Twitter.
The blast came a day after the Taliban called for a boycott of a Sept. 28 presidential election and threatened to attack election rallies.
Separately, security forces conducted raids on two Islamic State militant hideouts in Kabul overnight and killed two militants and seized a large quantity of explosives and bomb-making equipment, the National Directorate of Security (NDS) said.
Three members of the security forces were also killed, an agency spokesman said.
Both the U.S. peace envoy leading talks with the Taliban, and the Taliban reported significant progress this week in their talks in Qatar aimed at ending America’s longest war.
The militants control more territory than at any point since the United States bombed them out of power in 2001 and many government officials fear their war with the Taliban will not end if U.S. troops leave.
About 20,000 foreign troops, most of them American, are in Afghanistan as part of a U.S.-led NATO mission to train, assist and advise Afghan forces. Some U.S. forces carry out counter-terrorism operations.
President Donald Trump has announced his aim to end the war.