Care was originally expected to come out of the Barbarians at Twickenham, having been frozen out by Jones for four years since a game against Japan in which he was taken off at half-time.
The 35-year-old has 84 England caps and was the Premiership’s outstanding scrum-half this season, his campaign ending on Saturday when Quins lost to Saracens in the play-off.
He is one of six Quins called up to the team, although Joe Marler is not one of them. His companion Will Collier is recalled and hooker Jack Walker receives his first call. Regulars Marcus Smith, Alex Dombrandt and Joe Marchant are included.
Northampton Saints, the other losing semi-finalists, have five players called up: Lewis Ludlam, Courtney Lawes and Alex Mitchell, along with Fraser Dingwall and Tommy Freeman.
As they play the final on Saturday, Saracens and Leicester players are unavailable.
England travel to Australia for a three-Test series shortly after the game against the Barbarians.
“It’s a strong and diverse team,” Jones said. “There are a lot of exciting young players and a few experienced players who have another opportunity to shine.
“Everyone will have the chance to be part of the Australian tour team as we prepare for the Barbarians.”