Vince has been overlooked after failing to pass fifty in seven Tests this season, being guilty of a series of soft dismissals.
Mark Wood, who returns to the squad for the first time since undergoing ankle surgery in November, takes the place of injured bowler Steven Finn.
"Mark has had a couple of operations and with his hard work and advice from our medical team he's now able to take part in this series," national selector James Whitaker told the ECB website.
Joe Root and Chris Woakes, who were both impressive during the Test series, have been included, while Hampshire all-rounder Liam Dawson is the only uncapped player to have been named.
The five-match series starts in Southampton on Aug. 24, before matches at Lord's, Trent Bridge, Headlingly and Cardiff.
Squad:
Eoin Morgan (Cpt), Moeen Ali, Jonny Bairstow, Jos Buttler, Liam Dawson, Chris Jordan, Alex Hales, Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, Ben Stokes, David Willey, Chris Woakes, Mark Wood