The 27-year-old pulled out of his Korea Open quarter-final against America's Jenson Brooksby at the last minute on Friday.
The ATP said it was due to illness while Norrie had previously complained he was jet-lagged.
It means he will miss next week's Japan Open which will be a blow to his chances of sealing a place at the season-ending ATP Finals in Turin next month.
"Unfortunately I had a positive Covid test in Korea and wasn't able to compete in the rest of my matches. I have no symptoms and I am feeling 100%," he wrote on Twitter.
"I was really hoping to go to Tokyo but because of the quarantine period I will not be able to play there."