Team captains Matt Dawson and Phil Tufnell will also depart the long-running sports quiz show as part of a major shake-up.
Former professional tennis player Barker, 64, took over as presenter from commentator David Coleman in 1997.
She said: “I’ve absolutely loved my 24 years fronting A Question of Sport, it’s been my dream job.
“But I understand the BBC want to take the show in a new direction and I’m sad to say goodbye.”
Ex-England rugby player Dawson, 47, and former English international cricketer Tufnell, 54, have led their teams on the show for 16 and 12 years respectively.
Tufnell tweeted he was “going to miss it hugely”, adding: “thanks so much for all the lovely messages !!”
Thanks for all the lovely messages. I’m not sure how to respond so I’ll have a think 🤔 Needless to say I will miss @QuestionofSport immensely....
— Matt Dawson (@matt9dawson) September 13, 2020
Dawson said: “Thanks for all the lovely messages. I’m not sure how to respond so I’ll have a think. Needless to say I will miss @QuestionofSport immensely….”
Their final series together will be broadcast next year.
The new line-up is yet to be announced.
A BBC spokeswoman said: “We would like to thank Sue for her enormous contribution as the show’s longest reigning host over the last 24 years, and Matt and Phil for their excellent team captaincy over 16 and 12 years respectively.
“Together they have ensured A Question of Sport remains a firm favourite with the BBC One audience.
“Sue, Matt and Phil’s final series will be broadcast next year.”
Referred to by the BBC as “the world’s longest running TV sports quiz”, the first edition of A Question Of Sport aired in January 1970.
The move comes weeks after the BBC’s director-general Lord Hall was succeeded in the role by Tim Davie, the former chief executive of commercial arm BBC Studios.
