The 22-year-old was instructed to self-isolate after feeling unwell on Wednesday after an intra-squad warm-up match at the Ageas Bowl.
After being assessed by medical staff, he has been given the all clear to rejoin the group over the weekend.
A statement from the England and Wales Cricket Board read: "England's Sam Curran has tested negative following his Covid-19 test from yesterday.
"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.
"He will now return to training over the next 24-48 hours and will be closely monitored by the team doctor. Curran will receive a further Covid-19 test on Sunday with the rest of the playing and management group."