Peyton, 39, had arrived with reporter Peter Greste, when they were shot at outside their hotel. Suffolk-born Peyton was shot in the back while Greste escaped injury.
She was rushed to a local hospital where a bullet was removed, but she died of internal bleeding. Her death brings the total of journalists killed in the country since its government fell in 1991 to more than eight.
Helen Boaden, head of BBC News, said: "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."
Peyton had worked for the BBC for almost 12 years, during which time she had covered stories all across Africa. Tributes for the journalist came in from BBC director general Mark Thompson and the Foreign Office.
Thompson said: "I am profoundly shocked and saddened by the news of Kate Peyton's death today.
"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."
Somalia is ruled by warring tribal factions and until recently it was one of the only countries in the world to have no government. Its new government, the first since president Mohamed Siad Barre in 1991, is currently working in exile in Kenya with plans to return home with the assistance of thousands of African Union troops.
A spokesman for Somali President Abdulahi Yusuf Ahmed said Ms Peyton's death was "extremely shocking and extremely tragic", the Associated Press reported.
The BBC said it knew of no reason for the shooting, but in a country where guns are cheap and plentiful, little reason is ever needed.
Somalia was the subject of Ridley Scott's 2001 film 'Black Hawk Down', which told the story of failed attempts by the US and the UN to restore order in the country in an initiative that was known as Operation Restore Hope.
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