"After feeling unwell (Sunday) morning, Shane returned a positive lateral flow test and will isolate from the squad and support staff whilst he awaits PCR results.
"A second member of the team management is self-isolating after also returning a positive test. No players have been impacted."
The team took to Instagram to wish Warne well.
Warne returned to the UK recently to coach the London team and praised the nation for "learning to live" with coronavirus.
"I've been here for a few weeks and the country just opened up and they're having 50,000 odd cases a day but they're learning to live with it," Warne told Sky News Australia last week.
"It's been really interesting to watch how they've done it ... it's a very interesting time over here and watching how it all works.
"I think it's just a matter of getting on with it, get you double vax and get on and learn to live with it.
"No one over here wants to be locked down down anymore ... it's been so tough, I think they've just said enough's enough."
David Ripley, the Northamptonshire head coach and one of Spirit's assistants, acted as head coach in Warne's absence.
Warne is the second coach in the UK's inaugural Hundred cricket competition to test positive.
Trent Rockets head coach Andy Flower also tested positive last weekend and has already missed three matches.
Warne will miss Spirit's next match on Wednesday before the team has a week-long break.
