Nils Horner, 51, who also had British citizenship, had worked for Swedish Radio SR since 2001 as a foreign correspondent mostly in Asia and the Middle East, including Afghanistan and Baghdad.
Police said they were investigating whether it was an insurgent attack targeting a foreigner or whether the motive was personal.
Taliban spokesman Zabihullah Mujahid denied the group was responsible for the attack, which came two months after the Islamic militant movement staged a suicide bombing and shooting assault against a Lebanese restaurant that killed 13 foreigners and eight Afghans in the same area.
A guard at a restaurant across the street from where the attack happened said two young men approached the journalist as he was talking to his translator at about 11am on the side of the road. The area is home to several embassies.
The guard, Mohammad Zubair, said one of the men pulled out a pistol and shot Mr Horner in the head, causing him to collapse in a pool of blood. He said there was a single shot and the bullet then hit a nearby Mercedes Benz, which had a bullet hole.
The witness said he and other guards called to the police at a nearby checkpoint and they cordoned off the area.
Suicide bombings and other attacks are frequent in Kabul and elsewhere in Afghanistan as insurgents fight to undermine confidence in the Western-backed government. But assassinations of journalists and other foreigners in the capital are relatively rare.
Not including Mr Horner, at least 29 journalists have been killed in Afghanistan since 1992, most of them after the 2001 US-led ouster of the Taliban, according to the New York-based Committee to Protect Journalists.
Sayed Gul Agha Hashimi, the head of the Kabul Criminal Investigation Department, said police were questioning the journalist’s driver and translator as part of the investigation.
He said the journalist died while being treated at the hospital.
Swedish Embassy counsellor Christian Nilsson said the body had been transported to the morgue.
Anne Lagercrantz, head of news at Swedish Radio, said the newsroom was in deep shock.
She said Mr Horner spoke to the desk in Stockholm early today and they agreed that he would go out and do interviews ahead of the April 5 presidential election.
When people in the newsroom saw reports that a foreign journalist had been shot in Kabul, they tried to contact Mr Horner by email but got no response. They then called his mobile phone, and a doctor answered saying Mr Horner had been shot and killed, Ms Lagercrantz said.
Swedish Radio chief executive Cilla Benko said two men approached Mr Horner and shot him in the back of his head.
Ms Benko said Mr Horner was very safety conscious but was prepared to take risks. “This was his life,” Ms Benko said. “He didn’t want to do anything else.”
Swedish Radio officials said there were no known threats to Mr Horner.
The attack came as security in the capital was tight amid fears of violence in connection with the funeral of Afghanistan’s powerful vice president Mohammed Qasim Fahim.
Thousands of Afghans waving flags and chanting crowded into a Kabul cemetery and thronged an ambulance carrying Mr Fahim’s flag-covered coffin to the gravesite.
Mr Fahim, who died on Sunday at 57, was an ethnic Tajik and a leading commander in the Northern Alliance, which battled the Taliban for years and helped the US in ousting the Islamic militant movement.
His death came a month before elections to choose a successor to President Hamid Karzai, who is barred from seeking a third term.
At a funeral service earlier in the presidential palace, Mr Karzai lauded him for always promoting national interest.
“I lost my best friend and my brother,” Mr Karzai said, surrounded by tribal leaders and other Afghan dignitaries and foreign diplomats. “He was always with me in making important decisions on international and domestic issues.”
Mr Fahim was the top deputy of Ahmad Shah Massoud, the charismatic Northern Alliance commander who was killed in an al-Qaida suicide bombing two days before the September 11, 2001, attacks.
He was widely accused of marginalizing Pashtuns in the years after the Taliban were ousted, but later reconciled with Mr Karzai and was widely considered somebody who could mediate between factions.
Mr Karzai’s office said Mr Fahim - who held the rank of field marshal and had survived several assassination attempts, most recently in 2009 in northern Afghanistan - died of natural causes in Kabul.