Brunt, 37, retired from Test cricket earlier this year and will sit out three T20s and three ODIs to rest.
Outgoing head coach Lisa Keightley said: “After discussions with Katherine, she felt the best thing for her was to rest across both the series.
“We fully support that decision with a view to maximising her mental and physical recovery off the back of what has been an intense year.”
England are still without Heather Knight, who has undergone surgery on a hip injury, so are led by Nat Sciver. Bell for Brunt is the only change to the squad which competed at this summer’s Commonwealth Games.
Bell, who has played one Test and two ODIs, receives a first T20 call-up after a strong performance in the Hundred for Southern Brave.