"He has been monitored by the team doctor throughout and was tested for Covid-19 earlier today," the statement said, without mentioning when the result will be available.
Curran had scored 15 not out on the first day of England's intra-squad warm-up match.
The warm-up match is a part of England's preparation for the three-match Test series against the West Indies beginning here on July 8.
The Test series will mark the resumption of international cricket after the coronavirus-forced hiatus.
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