The 45-year-old Johnson, a two-time major championship winner who won The Open in 2015, was tested for the coronavirus after the final round of the John Deere Classic on Sunday, as were other players who were scheduled to make the trip to England for this week's tournament at Royal St. George's.
All of those players were given rapid-result PCR tests that came back in 90 minutes. Johnson, who tied for 34th in the John Deere Classic, tested positive and subsequently pulled out of The Open.
"I am disappointed to announce that I have tested positive for COVID-19 and will have to withdraw from the 2021 Open Championship," Johnson wrote in a statement on Twitter. "I look forward to returning to St. Andrews next year, a place where I have such wonderful memories. Good luck to all the competitors."
England's Sam Horsfield replaced Johnson in the field based on a reserve list taken from the Official World Golf Ranking.
On Sunday, Bubba Watson and this year's Masters champion Hideki Matsuyama both withdrew from The Open because of COVID-19 issues.
Watson, who is vaccinated against COVID-19, was identified as being a close contact of someone who tested positive for the virus. He was replaced in the field by Brendan Steele.
Matsuyama, meanwhile, said he pulled out of The Open because of a lack of practice time after his positive COVID-19 test at the Rocket Mortgage Classic earlier this month.
For various reasons, some related to COVID-19 testing and travel protocols, at least 16 players have opted out or withdrawn from The Open, which starts Thursday.