No claims of responsibility have been made for the explosion - in Kabul, Afghanistan - and the Taliban has issued a statement denying any involvement.
The centre is near to the Afghan Voice Agency, a media outlet which earlier reports had suggested could be the target.
The IS-linked Aamaq news agency said three bombs were used in the Thursday attack as well as a single suicide bomber who blew himself up inside the center.
Deputy interior ministry spokesman Nasrat Rahimi told AFP that the main blast was followed by two smaller bomb explosions that did not cause any casualties, and that the death toll is not final and "might" go up.
The attack has not yet been claimed by any insurgent group.
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A ceasefire that was supposed to go into effect on 23 December was shattered within hours when a Ukrainian solider was killed. Poroshenko insists Ukraine will use the weapons in a purely defensive manner to "rebuff the aggressor".
The attack, on 38th anniversary of the Soviet invasion, occurred during a panel discussion at the Tabian Social and Cultural Centre - with much of the crowd comprised of students and journalists, Reuters reported.
The Islamic State group affiliate in Afghanistan, in a statement on its Aamaq news agency, says it carried out the attack on a Shiite Muslim cultural center that killed at least 35 and wounded another 56.
Afghan Journalist Safety Committee (AJSC), a watchdog to promote safety of journalists in the country, condemned the attack on Twitter.
At least 40 people - reportedly including two children - have been killed after a suicide attack near a cultural center Afghanistan's capital. "But many governors and local officials are unable to accept the principle of media independence, and the police and military are implicated in several cases of violence against journalists", the note read.
Over the years, several worldwide media watchdogs have condemned the freedom and impunity given to the militants and other extremists to conduct such attacks against journalists.