Broad, who played for England at The Oval despite having a broken nose and two black eyes following an injury suffered during the fourth test match in Manchester, will miss the series to have specialist examination and treatment of a chronic right knee injury.
Test captain Alastair Cook, who led England’s triumphant recovery after they had trailed 1-0 following defeat in the second test, was selected to captain the one-day side.
Eleven of the 15 selected players were involved in the test series.
Batsmen Alex Hales and Eoin Morgan and bowlers Harry Gurney and James Tredwell have also been selected.
England squad: Alastair Cook (captain), Moeen Ali, James Anderson, Gary Balance, Ian Bell, Jos Buttler, Steven Finn, Harry Gurney, Alex Hales, Chris Jordan, Eoin Morgan, Joe Root, Ben Stokes, James Tredwell, Chris Woakes.
The series begins in Bristol next Monday- Reuters