Toulon centre Henson was suspended by the French club last month while they investigated an altercation involving the 29-year-old and team-mates following a league victory over Toulouse.
But Henson then gained a second chance, being restored to Toulon's squad and appearing as a substitute during the defeat against Montpellier on Saturday.
Number eight Andy Powell, though, has not made the squad.
Powell left Aviva Premiership side Wasps by mutual consent last week after the club probed a London bar-room brawl that left Powell nursing a head injury. He is currently without a club.
The squad includes five uncapped players, with Cardiff Blues flanker Sam Warburton named as captain.
Warburton will lead a side selected from the squad in the absence of Scarlets hooker Matthew Rees, who is rested.
Dragons pair Lloyd Burns and Toby Faletau,
Scarlets lock Lou Reed and centre Scott Williams, plus Ospreys prop Ryan Bevington are the uncapped players in the squad.
Henson has not played for Wales since the 2009 RBS 6 Nations Championship and fly-half Stephen Jones is set to win his 100th cap.
Gatland said: "We have selected some exciting youngsters who have been chosen on form in the knowledge that there are a few players who are being rested or are injured for this game, but it means they have a chance to impress.
"It's a great opportunity for us to look at some players that have been hitting their form over the last few weeks.
"These are really exciting times for us as a squad. The Rugby World Cup is on the horizon and we begin our preparations with this first up match against the Barbarians before two intensive training camps in Poland and then our final three matches in August.
"Sam Warburton takes over the captaincy mantle from Matthew Rees, who is rested.
Sam is one of the leaders in the squad and will benefit from the experience of captaining the side after having such an impressive Six Nations campaign."
Wales squad - forwards: P James (Ospreys), J Yapp (Cardiff Blues), R Bevington (Ospreys), S Andrews (Cardiff Blues), H Bennett (Ospreys), R Hibbard (Ospreys), L Burns (Newport Gwent Dragons), A-W Jones (Ospreys), R Jones (Ospreys), L Charteris (Newport Gwent Dragons), L Reed (Scarlets), D Lydiate (Newport Gwent Dragons), T Faletau (Newport Gwent Dragons), J Turnbull (Scarlets), S Warburton (Cardiff Blues, capt).
Backs: M Stoddart (Scarlets), G North (Scarlets), A Brew (Newport Gwent Dragons), S Williams (Ospreys), J Davies (Scarlets), S Williams (Scarlets), G Henson (Toulon), S Jones (Scarlets), R Priestland (Scarlets), M Phillips (Ospreys), T Knoyle (Scarlets).
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