“In choosing this place of dialogue, it is culture and creation that the terrorists have targeted,” Hollande said.
The blast killed one person and injured about 15 others, officials said.
The German government on Friday announced that one of its nationals had died.
No French citizens were among the victims, the French foreign affairs ministry reported, while Afghan news media say that five or six of the injured were local journalists.
There were 300-400 people in the audience of the play Heart Beat; the silence after explosion according to Kabul university professor Shafigh Shargh, who was one of them.
“It was supposed to be about suicide attacks and violence in Afghanistan,” he told France 24 TV. “After a few minutes the room was dark and we saw a huge explosion. We were all thrown to the ground.”
People ran out of the room but were unable to escape through the windows that were sealed shut, he said.
“We had to go back through the theatre. There was lots of dust and smoke. The roof had fallen in. I saw dismembered corpses and dozens of injured.”
Taliban spokesperson Zabihullah Mujahid claimed responsibility for the attack and for another that killed six soldiers earlier in the day.
The play was desecrating Islamic values” and making “propaganda against jihad”, he said.
“All possible light must be shone on this barbarous act,” a statement from Foreign Affairs Minister Laurent Fabius said. “Its authors must be identified and brought to justice.”
Prime Minister Manuel Valls also dubbed the bombing “barbaric”.
“In attacking a symbol of culture and the universality of values that France holds dear, the terrorists again show that they have a message of hatred and obscurantism,” he said in a statement.
The United Nations Security Council issued a unanimous statement condemning both attacks, voicing “"serious concern at the threats posed by the Taliban, Al-Qaeda and other terrorist and extremist groups, and illegal armed groups" as foreign troops prepare to end their combat mission in Afghanistan.
Originally opened in 1970, the cultural centre was forced to close between 1983 and 2002 as Afghanistan was torn apart by a series of wars.
It reopened in 2003 and the auditorium and media library were revamped in 2010.
The Lycée Istaqlal, which is on the same campus, is one of Kabul’s most respected schools.
One of its best known former pupils was anti-Soviet and anti-Taliban leader, Ahmed Shah Masood.