Sibley had scores of four and 29 in the first Test in Centurion, which South Africa won by 107 runs to take a 1-0 lead in the four-match series, but will now be a doubt for the second game starting in Cape Town on Friday.
The Board had better news about seamer Chris Woakes and spinner Jack Leach, who have shown signs of improvement and are out of quarantine at the team hotel.
Captain Joe Root and wicketkeeper Jos Buttler both felt unwell during the first Test, while seamers Stuart Broad and Jofra Archer had no match practice in the build-up to the game after being laid low.
Ben Stokes was also treated for dehydration on the opening day in Pretoria, while middle-order batsman Ollie Pope missed the game altogether and was replaced by Jonny Bairstow, and seamer Mark Wood also fell ill.
Batsman Joe Denly was also unwell in the build-up to the first Test and is one of 17 players and support staff who have been struck down at some point on the tour but skipper Root has refused to blame the illness for their opening defeat.
“We are not going to hide behind that as an excuse but a lot of our squad have been taken ill over the last two weeks,” Root told reporters on Sunday.
“There are certain things you try to control but some that you can’t. We’ve done very well that it did not affect as many it could.”