Wright was called up for Wednesday's sixth match at The Oval and Saturday's finale at Lord's because of injuries to Ravi Bopara, Andrew Flintoff and Chris Tremlett, the England and Wales Cricket Board said in a statement on Monday.
The 22-year-old Wright was recently selected for this month's Twenty20 World Cup in South Africa.
Seamer Ryan Sidebottom has also been cleared to rejoin the squad after recovering from his side strain.
The injuries to all-rounders Flintoff (ankle) and Bopara (thumb) will be reassessed by England's medical team on Tuesday.
Paceman Tremlett will miss Wednesday's game with a foot injury but could be fit for Lord's.
England are 3-2 up in the seven-match series.
