Morris, who is 21 this week, takes over from Bristol Shoguns tighthead Julian White, who is still experiencing problems with his left knee that he injured during a club game with Bristol.
White's absence is a huge blow for England, and continues something of a front-row injury jinx.
Gloucester props Phil Vickery and Trevor Woodman are currently sidelined, as is Saracens' David Flatman, while 100 times-capped Jason Leonard damaged his hamstring during last weekend's victory over France.
Leonard is also out of action, meaning a recall to the starting XV for Leicester's Graham Rowntree.
Morris was on the bench for two of England's Tests during the autumn series - against Australia and South Africa - but did not feature.
"Robbie is not a new player to us," said Woodward. "He went to Argentina with us last summer, and he was also around for the autumn Tests.
"He will be packing down alongside his club team-mate Steve Thompson, and we are confident that he will step up to the plate and really perform."
Kyran Bracken will start at scrum-half as replacement for Andy Gomarsall. Lawrence Dallaglio, who replaced the injured Lewis Moody in the victory over France will continue in the back-row.
England team to play Wales in Cardiff:
Backs: J Robinson (Sale Sharks), D Luger (Harlequins), W Greenwood (Harlequins), C Hodgson (Sale Sharks), B Cohen (Northampton), J Wilkinson (Newcastle), K Bracken (Saracens);
Forwards: G Rowntree (Leicester), S Thompson (Northampton), R Morris (Northampton), M Johnson (Leicester, capt), B Kay (Leicester), R Hill (Saracens), N Back (Leicester), L Dallaglio (Wasps).
Replacements: M Regan (Leeds), M Worsley (London Irish), D Grewcock (Bath), J Worsley (Wasps), A Gomarsall (Gloucester), P Christophers (Bristol Shoguns), J Simpson-Daniel (Gloucester).