Lancashire batsman Livingstone, who scored 129 from 83 balls for England Lions against South Africa A last week, is one of five uncapped players named.
Mason Crane, Dawid Malan, Tom Curran and Craig Overton are the other four players yet to make their debut.
The three-match series starts in Southampton on 21 June.
England lost their last Twenty20 series 2-1 to India in February.
Moeen Ali, Jake Ball, Adil Rashid, Joe Root and Ben Stokes have been rested and will instead play for their respective counties in the inaugural day-night round of the County Championship, which starts on 26 June.
This will allow them to gain experience of playing with the pink Dukes balls that will be used for the first day-night Test to be played in England, against West Indies at Edgbaston in August.
Sussex fast bowler Tymal Mills, meanwhile, has been ruled out with a back injury, but Durham seamer Mark Wood returns after missing the India series through injury.
Middlesex opener Malan, Surrey paceman Curran and Somerset all-rounder Overton have previously been included in England squads, while Hampshire leg-spinner Crane is called up after impressing in the North-South series in March.
Overton will replace Wood in the squad after the first match, while wicketkeeper Jonny Bairstow will be available for the first two matches before returning to Yorkshire.
Jason Roy, who has managed just 18 runs in three innings for England in the ongoing Champions Trophy, is named in the squad.
Chairman of selectors James Whitaker said: "The squad has an exciting blend of youth and experience and we are looking forward to a competitive series against strong opposition.
"With five uncapped players selected, there is undoubted talent coming through the system and we are excited to see some of these players showcase their skills at the highest level."
BBC Radio Lancashire's Scott Read
There is a touch of Kevin Pietersen about Liam Livingstone when he gets onto the front foot to pull through mid-wicket.
He is a powerful, destructive batsman who in white-ball cricket has the ability to take games away from the opposition and is great fun to watch.
Liam Livingstone has been given his first senior international call-up as England rest five players for the Twenty20 series against South Africa.