Veaila, a New Zealand-born centre who has yet to play in the NRL, has been in isolation since Monday and returned a positive finding on Wednesday morning after players and staff were sent for testing.
The rest of the Knights squad and essential training staff who have returned negative results went back to training on Wednesday.
"All will be required to adhere to strict processes and protocols," the Knights said in a statement.
"The Knights will continue to work through all mandatory guidelines and health orders with all relevant bodies, to ensure best practise is applied."
The positive case for Vae'lia follows a couple of cases from a NSW Blues camp which took place over the weekend.
Members of both an Emerging Blues men's squad and the Sky Blues women's camp recorded positive cases, forcing NSW assistant coaches Andrew Johns, Danny Buderus and Paul McGregor and more than 80 players to go into isolation.
Meanwhile, three players from the Newcastle Jets are believed to have tested positive.
Jets midfielder Angus Thurgate and reserve goalkeeper Noah James are understood to have returned positive results, along with defender Kirsty Fenton from the club's women's side.
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