Kate Peyton, 39, and reporter Peter Greste had just arrived in the capital Mogadishu when she was hit. Mr Greste was not injured.
Ms Peyton was taken to hospital, where she had an operation on a bullet wound to her back, but died later of internal bleeding, the BBC said.
Head of BBC News Helen Boaden said 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."
'Shock'
BBC director general Mark Thompson said he was "profoundly shocked and saddened" by Ms Peyton's death.
"Kate had worked for the BBC since 1993 and was dedicated to covering news across the African continent."
The Foreign Office has also paid tribute to Ms Peyton.
"She had travelled with the foreign secretary abroad and was well known to our media staff wherever she went," it said in a statement.
A spokesman for Somali President Abdullahi Yusuf Ahmed said Ms Peyton's death was "extremely shocking and extremely tragic", the Associated Press reported.
Yusuf Ismail spoke to the news agency from Kenya where the exiled government is currently based.
'Cowardly act'
Details about the incident were still unclear, but the BBC said it was believed to have happened outside the Sahafi Hotel.
Ms Peyton, who grew up in Suffolk, had spent the past 10 years in Africa and was based in Johannesburg. She had worked for the BBC as a producer and reporter since 1993.
She also worked as a producer and trainer for the South African Broadcasting Corporation in Johannesburg.
Her friend and colleague BBC correspondent Fergal Keane said Ms Peyton was "the kindest, gentlest human being to work with and to have as a friend and I will always treasure her laughter and stories".
"She devoted a large part of her life in trying to telling the truth about Africa," he added.
Investigation call
The National Union of Journalists, of which Ms Peyton was a member, condemned the killing and called for a "full investigation" into the circumstances.
General secretary Jeremy Dear said: "This dreadful shooting, coming just after the announcement that more journalists were killed last year than in any year before, reminds us just how dangerous reporting has become."
He said one reason for the rising death toll was because "the killers are rarely pursued and brought to justice".
"We will ask the UK government to press the UN as well as the Somali authorities to pursue these killers," he said.
Ultimi Articoli
Neve in pianura tra venerdì 23 e domenica 25 gennaio — cosa è realmente atteso al Nord Italia
Se ne va Valentino, l'ultimo imperatore della moda mondiale
La mortalità per cancro cala in Europa – tassi in diminuzione nel 2026, ma persistono disparità
Carofiglio porta — Elogio dell'ignoranza e dell'errore — al Teatro Manzoni
Teatro per tutta la famiglia: “Inside and Out of Me 2” tra ironia e interazione
Dogliani celebra quindici anni di Festival della TV con “Dialoghi Coraggiosi”
Sesto San Giovanni — 180 milioni dalla Regione per l’ospedale che rafforza la Città della Salute
Triennale Milano — Una settimana di libri, musica, danza e arti sonore dal 20 al 25 gennaio
A febbraio la corsa alle iscrizioni nidi – Milano apre il portale per 2026/2027