The 27-year-old Gloucester fullback has had a stand-out season since joining from Bristol last season, scoring twice in his last four games and being named man of the match in the Challenge Cup semi-final win over Newcastle Falcons.
Woodward, who qualifies for England through his grandmother, earlier played for Wellington, and the Hurricanes in Super Rugby.
England will play South Africa in three tests, in Johannesburg on June 9, Bloemfontein on June 16, and Cape Town on June 23.
England
Backs: Mike Brown (Harlequins), Elliot Daly (Wasps), Nathan Earle (Saracens) *, Jonny May (Leicester Tigers), Denny Solomona (Sale Sharks), Danny Cipriani (Wasps), Owen Farrell (Saracens), George Ford (Leicester Tigers), Alex Lozowski (Saracens), Cameron Redpath (Sale Sharks) *, Dan Robson (Wasps) *, Henry Slade (Exeter Chiefs), Ben Spencer (Saracens) *, Ben Te'o (Worcester Warriors), Ben Youngs (Leicester Tigers).
Forwards: Tom Curry (Sale Sharks), Ben Earl (Saracens) *, Jonny Hill (Exeter Chiefs) *, Nick Isiekwe (Saracens), Maro Itoje (Saracens) , Joe Launchbury (Wasps), Chris Robshaw (Harlequins), Brad Shields (Hurricanes/ Wasps) *, Sam Simmonds (Exeter Chiefs), Billy Vunipola (Saracens), Jack Willis (Wasps) *, Mark Wilson (Newcastle), Luke Cowan-Dickie (Exeter Chiefs), Ellis Genge (Leicester Tigers), Jamie George (Saracens), Joe Marler (Harlequins), Kyle Sinckler (Harlequins), Mako Vunipola (Saracens), Harry Williams (Exeter Chiefs)
* - uncapped