Stone has been hampered by stiffness in his lower left back since taking part in a practice session on Sunday.
Stone had hoped to make his Test debut in the three-match series, but the Warwickshire seamer will have to wait for his maiden five-day appearance.
"Following the result of scans, Olly Stone has sustained a bone stress injury to the left lower back. He will return home from the Caribbean later this week and have further tests in the UK," a statement from the England and Wales Cricket Board said on Wednesday.
Stone impressed with his speed and hostility during four appearances in England's one-day series win against Sri Lanka in October.
But the back problem is the latest injury blow for Stone, who saw his promising career interrupted for 18 months with an anterior cruciate ligament problem.
He has been restricted to just 34 first-class matches since debuting in 2012. Ashley Giles, previously director of cricket at Warwickshire and recently appointed to the equivalent role with the ECB, warned selectors last year not to work Stone too hard.
He described the player as a "Ferrari" and cautioned against his over-use. England have yet to name a replacement but the likes of Jamie Overton, Jamie Porter and Mark Wood are likely to come under consideration by selectors.
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