Yorkshire said in a statement on Wednesday that Matthew Fisher, Tom Kohler-Cadmore, Josh Poysden and Willey had been advised to self-isolate for two weeks after a positive test was received within the squad.
Willey later confirmed he had tested positive.
"My wife and I received positive COVID test results. Gutted to be missing the remaining games," the 30-year-old wrote on Twitter.
"Even more devastated that having been in contact with the other three lads Saturday morning (before we had symptoms) means they're at risk and unavailable too."
The four players missed Yorkshire's 43-run defeat by Durham on Wednesday and will sit out games against Lancashire later on Thursday and Derbyshire on Sunday.
Yorkshire are fifth in the North Group with six points from eight matches. (Reporting by Arvind Sriram in Bengaluru; Editing by Peter Rutherford )