Brent Renaud, 50, was a journalist and filmmaker who was working in the region for Time.
Kyiv’s police chief Andriy Nebytov said he had been targeted by Russian soldiers. Two other journalists were injured and taken to hospital.
It is the first reported death of a foreign journalist covering the war in Ukraine.
One of the injured journalists, Juan Arredondo, told an Italian reporter he had been with Renaud when they came under fire.
“We were across one of the first bridges in Irpin, going to film other refugees leaving, and we got into a car”, he said in a video published on Twitter.
“Somebody offered to take us to the other bridge and we crossed a checkpoint, and they start shooting at us. So the driver turned around, and they kept shooting; there’s two of us. My friend is Brent Renaud, and he’s been shot and left behind… I saw him being shot in the neck.”
Photographs are circulating online showing a press ID for Renaud issued by the New York Times.
In a statement, the newspaper said it was “deeply saddened” to hear of Renaud’s death but that he had not been working for the newspaper in Ukraine.
Renaud last worked for the publication in 2015, the Times said, and the press ID he was wearing in Ukraine had been issued years ago.
Time editor-in-chief and CEO Edward Felsenthal and Ian Orefice, the president and chief operating officer of Time and Time Studios, said they were “devastated by the loss”.
“As an award-winning filmmaker and journalist, Brent tackled the toughest stories around the world often alongside his brother Craig Renaud,” the statement said.
Renaud had reported from Afghanistan, Iraq and Haiti. He won a Peabody Award for his work on a 2014 series on Chicago schools, Last Chance High.
He often worked alongside his brother, Craig, also a filmmaker. It is not known whether Craig also travelled to Ukraine.
Renaud’s death comes less than two weeks after Ukrainian journalist Yevhenii Skaum, a camera operator for the Ukrainian television channel LIVE, was killed when a TV transmission tower in Kviv was hit by shelling.
A few days later, a British journalist covering the war in Ukraine was shot and wounded after coming under fire in Kyiv.