Fox News in a statement only announced the death of Zakrzewski, an Irish citizen. Ukrainian officials and Fox News reporters confirmed that Kuvshynova was also killed in the attack.
"RIP Pierre and Sasha," the Fox News Pentagon correspondent, Lucas Tomlinson, wrote on Twitter, using a diminutive name for the producer, and sharing a recent picture of the two, smiling with Hall.
Zakrzewski, 55, and Kuvshynova, 24, died "as a result of artillery shelling by Russian troops in the north-eastern part of the village of Gorenka", Ukrainian website kp.ua said.
The news follows the death in Ukraine on Sunday of Brent Renaud, an American film-maker, who was shot in an area near where the Fox journalists were attacked.
Fox News had announced Hall’s injury on Monday, the reporter "was injured while newsgathering outside of Kyiv in Ukraine".
Fox News’ chief executive, Suzanne Scott, said: "Pierre was killed in Horenka, outside of Kyiv, Ukraine. Pierre was with Benjamin Hall yesterday ... when their vehicle was struck by incoming fire.