The bomber targeted a play at a French-financed school late on Thursday, killing several people.
The Taliban have claimed responsibility for the suicide attack.
"A suicide bomber blew himself up among the audience in Istiqlal High School," said Afghan interior ministry spokesman Sediqi Sediqqi.
The auditorium at the school, which is attached to Kabul's long-established French cultural centre, was packed at the time of the attack.
Fifteen people were rushed to hospital including Doctor Ahmad Naser Sarmast, a highly regarded Afghan Australian musician, who was knocked unconscious.
"I was watching the drama and my students were playing some music when I heard a blast. I thought it was part of the drama but I touched my head and saw it was bleeding, and then I fell down. I don't know what happened next,” Dr Sarmast said in the aftermath of the attack.
Dr Sarmast works between Monash University in Melbourne and the Musicians' Institute of Afghanistan.
He's responsible for helping to bring music back onto the streets of Kabul after the Taliban banned it.
He recently appeared in an SBS documentary, Dr Sarmast’s Music School, about revitalising the music scene in Afghanistan, which was destroyed by the Taliban prior to 2001.
A 17- year-old suicide bomber carried out the attack on Thursday night's performance.
Earlier on Thursday bombers targeted a bus carrying Afghan troops in Tangi Tarakhil on the outskirts of the capital.
"As a result of the (first) attack, six Afghan army staff were martyred and 10 others were wounded," senior Kabul police official General Farid Afzail said.
Taliban spokesman Zabihullah Mujahid claimed both bombings in separate email statements sent to media.
He said the theatre show was "desecrating Islamic values" and "propaganda against jihad", particularly suicide attacks.
Afzali and the interior ministry said one foreign national was killed, without giving further details.
But French Foreign Minister Laurent Fabius said the "barbaric" attack had left several people dead.
"I firmly condemn this terrorist act which caused the death of several people and left many injured. There were no French victims," Fabius said in a statement.
French President Francois Hollande condemned the bombing as "heinous" and said it was an assault on "culture and creativity."
"It is a place of tolerance, of dialogue between the cultures and it is this symbol that the terrorists wanted to target,” said Romain Nadal, French Ministry of Foreign Affairs.
“But as the French President and Prime Minister stated, France will not give up its cultural and educational cooperation with the Afghan people and they expect our support."
NATO forces are preparing to pull out of Afghanistan within weeks.
Kabul has been hit by a spate of deadly attacks in recent weeks, heightening concerns that Afghanistan could tip into a spiral of violence as the US-led military presence declines.