The Islamic State group (IS) claimed responsibility for the gruesome assault, which happened in the same building as the Afghan Voice Agency, a media outlet which earlier reports had suggested could have been the target.
Deputy interior ministry spokesman Nasrat Rahimi told AFP the attack -- the deadliest since a Shia mosque bombing in October that killed more than 50 worshippers -- was aimed at the Tabayan cultural centre in the west of the city.
"The suicide attacker detonated himself during a gathering at Tabayan cultural centre causing a lot of casualties," Rahimi said.
The main explosion was followed by two smaller bomb blasts as victims and survivors were leaving the scene.
Rahimi said the gathering was organised to mark the 38th anniversary of Soviet invasion in Afghanistan. An Afghan Voice Agency journalist told AFP that more than 100 people were at the event in the building's basement.
There were chaotic scenes at the Istiqlal hospital where ambulances and police pickups brought victims, including women and children. Many of them had suffered severe burns to their faces and bodies, as well as shrapnel wounds, AFP reporters said.
Visibly distressed relatives searching for their loved ones inside the medical facility slapped their heads in fury as they cried and cursed the government for seemingly being unable to end the regular carnage on their streets.
Some were so distraught they crawled on the ground pulling their hair.
AFP reporters saw more than a dozen badly burned bodies lying on the floor in a room inside the hospital and wooden coffins being delivered so families could take away the bodies of their loved ones.
Kabul has become one of the deadliest places in war-torn Afghanistan for civilians in recent months, as the Taliban step up their attacks and IS seeks to expand its presence in the country.
Thursday's assault comes days after a suicide bomber killed six civilians in an attack near an Afghan intelligence agency compound in the city, which was claimed by IS.
The Middle Eastern jihadist group has gained ground in Afghanistan since it first appeared in the region in 2015, and has scaled up its attacks in Kabul, including on security installations and the country's Shia minority.
'Big boom'
A man attending the anniversary ceremony at Tabayan said he heard a "big boom".
"We do not know the numbers (of casualties). When the explosion happened we immediately fled," he told Tolo News.
Mohammad Hasan Rezayee, a university student who was also at the ceremony, told Tolo News he had suffered burns to his face in the blast.
"We were inside the hall in the second row when there was an explosion behind us. I did not see the bomber," he said from his hospital bed.
"After the blast, there was fire and smoke inside the building and everyone was pleading for help."
The attack drew international condemnation, with NATO's Resolute Support mission in Afghanistan describing it as "heinous". Amnesty International said it was further evidence that Kabul was not safe.
"The European governments who insist on this dangerous fiction by forcibly returning Afghans are putting their lives in danger," Amnesty International's South Asia director Biraj Patnaik said in a statement.
Photos posted on Afghan Voice Agency's Facebook page showed the inside of a compound with debris and bodies lying on the ground.
Security in Kabul has been ramped up since May 31 when a massive truck bomb ripped through the diplomatic quarter, killing some 150 people and wounding around 400 others -- mostly civilians. No group has yet claimed that attack.
Religious attacks in Afghanistan have skyrocketed in the past two years with the minority Shia community the main target, the United Nations said in November.
IS, a Sunni extremist group, has claimed most of the attacks on Shia worshippers as it seeks to stir up sectarian violence in the country.
The Afghan media has also previously been targeted by militants, underlining the risks faced by journalists in the war-torn country.