A statement from the BBC said Ms Peyton was taken to hospital, where she had an operation on a bullet wound to her back. It was later reported she died from internal bleeding.
The head of BBC News, Helen Boaden, paid tribute to Ms Peyton, saying she would be "greatly missed". "Kate was one of our most experienced and respected foreign affairs producers who had worked all over Africa and all over the world.
"She will be greatly missed, both professionally and personally. We are in touch with the family and are doing everything we can to support them at this terrible time."
The director-general, Mark Thompson, said: "I am profoundly shocked and saddened by the news of Kate Peyton's death. Kate had worked for the BBC since 1993 and was dedicated to covering news across the African continent. All our thoughts are with her family and friends at this time."
Details about the incident were still unclear, but the BBC said it was believed to have happened outside the Sahafi Hotel. Ms Peyton has spent the past 10 years in Africa.Reuse content