A statement on Thursday revealed that the all-rounder experienced “sickness and diarrhea” overnight.
The ECB added that the 22-year-old has since been feeling better but was tested for coronavirus earlier on Thursday.
Curran has been self-isolating in his room at Southampton’s Ageas Bowl since he first felt ill and will continue to do so as he awaits the result of his Covid-19 test.
He will also continue to be monitored by England’s team doctor.
England take on the West Indies in a three-Test series this month, with the first match beginning on 8 July. The final match will end on 28 July.
Test Captain Joe Root will miss the first Test due to the impending birth of his second child, and vice-captain Ben Stokes will lead the side for the first time as a result.
Jos Buttler will assume vice-captaincy duties.