Essex batsman Bopara will get the chance to push his claims for a Test recall in the four-day fixture against the tourists, which gets underway on May 19.
The 25-year-old was part of England's squad that won the ICC World Twenty20 tournament in the Caribbean.
He played in one match during their victorious campaign having missed the start of the domestic season due to his Indian Premier League commitments.
Bopara has not featured in a Test match since England's defeat to Australia at Headingley during last year's Ashes series on home soil.
Hampshire opener Carberry, who made his international debut during the winter tour of Bangladesh, has been ruled out due to a bruised bone in his right foot.
Bopara's county colleague Alastair Cook has been chosen to captain the Lions for the match at Derby against the Tigers.