Morgan was replaced by Moeen Ali for the third match of the series after pulling up in the warm-up. England went on to suffer a 20-run defeat meaning they trail Windies 2-1 heading into the final two games.
Following the clash at the Kensington Oval, examinations on Morgan revealed a slight issue with the 35-year-old's thigh. Subsequently, England have decided not to risk the captain for this weekend's double-header in Barbados.
An England and Wales Cricket Board spokesperson confirmed Moeen, as Morgan's deputy on this whistle-stop T20 tour, will lead the side on Saturday and Sunday.
An ECB statement read: "England men's captain Eoin Morgan will miss the final two matches of the international Twenty20 series against the West Indies with a low-grade quadriceps injury.
"Morgan sat out the third T20 in Barbados on Wednesday night after he felt pain in his right quad during the warm-up.
"Follow-up testing revealed he sustained a right thigh muscle injury which, whilst relatively minor, will prevent him from playing further games during the current tour."
In other news for England, Liam Livingstone is expected to be fit for the penultimate T20 having been briefly treated for acid reflux while batting on Wednesday in his comeback from oesophagitis.