An attacker on a motorbike carried out the first explosion on Monday morning in Kabul's Shashdarak district.
About 15 minutes later, after people and reporters had gathered at the scene, there was a second explosion.
AFP said its chief photographer, Shah Marai, had been killed.
In a tweet, the news agency said the second blast had deliberately targeted the group of journalists.
"The bomber disguised himself as a journalist and detonated himself among the crowd," AFP quoted a police spokesman as saying.
The Shashdarak district houses the defence ministry, intelligence service, and a Nato compound.
Dozens of people are also reported to have been injured in the twin explosions.
Shah Marai started work as a driver with AFP in the 1990s, during the era of the Taliban.
His interest in the world, his curiosity and love for photography resulted in AFP sending him to France for training.
When he came back, he turned his wonderful eye to capturing moments of humanity during the most shocking ordeals of his city, Kabul.
Photo by Shah Marai: An Afghan woman asks for donations, Kabul, 2009
One of his most iconic photographs was from an attack on a Shia mosque last year: a picture of a child just standing stunned with police pointing at him to leave the mosque because the attacker was still inside. But the child was looking for his father.
Throughout it all Shah Marai was calm, smiling and positive. He was never scared of danger.
Photo by Shah Marai: An Afghan girl scavenges for recyclables, 2011
But he was deeply affected when his good friend and fellow journalist Sardar Ahmad was murdered a few years ago in another Kabul attack at the Serena hotel.
I have known Shah Marai since I was a child and we found ourselves both working for the media here in Kabul, always meeting at the sites of tragedy.
He was also a friend to many others in Kabul's journalistic community and we are all mourning him now.
No group has yet said it carried out the attacks, but bombings in the Afghan capital are not uncommon.
Earlier in April, a suicide bomb at a voter registration killed almost 60 people and injured 119, in an attack claimed by the Islamic State group.
Both IS and the Taliban remain active in the country, of which only 30% is under full government control, according to BBC research published earlier this year.
Last week, the Taliban announced its annual spring offensive, saying it would be targeting foreign forces.
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