The 30-year-old has been deemed a close contact of the individual in question and must now isolate for ten days.
Konta had been due to start her campaign in the first round against the Czech Republic’s Katerina Siniakova on Tuesday.
Her place in the draw will be taken by China’s Yafan Wang.
Konta’s preparation on grass had seemed to be going well as she won her fourth WTA Tour title at the Viking Open in Nottingham, but she subsequently withdrew from warm-up events in Birmingham and Nottingham because of a knee problem.
“A member of Johanna Konta’s team presented with COVID-19 symptoms this morning, and immediately isolated and undertook a PCR test in accordance with The Championships’ testing protocols,” a statement said.
“A positive result was returned which resulted in the AELTC, together with Public Health England, identifying Johanna Konta to be a close contact. In line with government legislation, she is required to self-isolate for 10 days and therefore is withdrawn from The Championships.”
Konta, who was due to be the 27th seed, was a quarter-finalist at SW19 the last time the tournament was staged, in 2019, with her best ever run coming in 2017, when she reached the semi-finals.