The Taliban denied responsibility for the killing in an upmarket district close to a Lebanese restaurant in the Afghan capital, where the militants launched a suicide attack that killed 21 people, including 13 foreigners, in January.
The Swedish ambassador to Afghanistan Peter Semneby identified the dead man as radio journalist Nils Horner.
"Unfortunately we just have received confirmation that Nils Horner, who was correspondent for Swedish national radio, was shot and killed in Kabul this morning," ambassador Peter Semneby said.
"We understand he had British nationality in addition to his Swedish nationality. His family has been informed."
A witness at the scene described hearing a single gunshot before seeing the victim fall to the ground and a doctor at Kabul's emergency hospital said he was dead on arrival.
"There were two guys who ran away. They were perhaps in their 20s and security guards chased them as they ran away," the witness told AFP on condition of anonymity.
Security forces rushed to the scene and cordoned off the street, where there was blood visible on the ground.
The attack came as many of the Afghan capital's security forces were occupied with the funeral of Vice-President Marshal Mohammad Qasim Fahim, who died on Sunday.
The Taliban, who have led the insurgency against the Western-backed government of President Hamid Karzai since being toppled from power in 2001, denied the attack.
"We checked with our mujahideen and they are not involved," Taliban spokesman Zabiullah Mujahid told AFP.
"We don't take responsibility for this incident." The attack comes less than a month before presidential elections in Afghanistan on April 5 and the withdrawal of Nato combat troops by the end of this year after 13 years of fighting the Taliban.
Foreigners have been targeted before at guesthouses, luxury hotels and embassies in the heavily guarded city, but few have been gunned down on the street.
The attack in January on the Taverna du Liban, a popular social venue for foreigners, badly shook Kabul's sizeable community of expatriate diplomats, aid workers and journalists.
It was the deadliest attack on foreign civilians since the fall of the Taliban.
Among the dead were three Americans, two British citizens, two Canadians, the International Monetary Fund's head of mission, and the restaurant's Lebanese owner.
One attacker detonated his suicide vest at the fortified entrance to the restaurant before two other militants stormed inside and gunned down diners and staff.
The next president will face a testing new era as the Afghan army and police attempt to impose security without Nato assistance and as international funding declines.
Among the front-runners in the election are Abdullah Abdullah, who came second in 2009, former foreign minister Zalmai Rassoul and former World Bank economist Ashraf Ghani.