"The Surrey all-rounder, who had a sickness bug has recovered and is currently missing the intra-group three-day match, which ends today, has been self-isolating in his room at the Ageas Bowl," the ECB said in a statement.
"He will now return to training over the next 24-48 hours and will be closely monitored by the team doctor," it added.
Curran will undergo another test for Covid-19 on Sunday along with the rest of the squad.
He had scored 15 not out on the first day of England's intra-squad warm-up match before falling ill.
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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