Thirlby said the positive test was a "shock" as she hadn't shown any symptons of coronavirus. She's now in self isolation.
All 16 players and other coaching staff and management have returned two negative COVID-19 tests.
"I am extremely disappointed to not be travelling....we have been taking every precaution; remaining in small bubbles during training, having staff wear masks at all times, as well as players wearing masks when not on court, social distancing, doing temperature checks on arrival, plus self-isolating at home and undergoing a pre-flight testing plan prior to travelling," she said.
"Whilst I'm still awaiting my second set of test results, we cannot take any risks as the safety of all involved is the priority."
Thirlby will still help the side out coaching on-line. "I will do all I can to support them remotely."
When the England side arrives in New Zealand they will go into two weeks isolation, similarly to the Australian rugby side ahead of their Bledisloe Cup series agianst the All Blacks.
The three test series between England and New Zealand starts in Hamilton on October 28th.