Premier Annastacia Palaszczuk has ordered a lockdown of the city's hospitals, aged care facilities, prisons and disability services from 12pm to prevent the virus spreading.
She says the 26-year-old man lives in Stafford and tested positive on Thursday, but he's been infectious in the community since last Friday.
"We wanted to let the public know as soon as possible," Ms Palaszczuk told reporters.
"It is absolutely imperative over the next few days if you are sick and unwell to go and get tested, it is absolutely critical."
Chief Health Officer Jeannette Young said the man visited a number of venues in the past week, including the Carindale Shopping Centre and a Baskin-Robbins outlet at Everton Park on March 20
The next day he visited a supermarket and an Italian restaurant in Newstead.
On March 22 he went to work in Paddington, where he's landscaper, and visited a Guzman y Gomez drive-through.
"Anyone who's been to any of these venues in those specific time frames, I want you to come forward and get tested whether or not you've got symptoms, and to remain in isolation until you get a negative result," Dr Young said.
The man may be linked to an earlier case in a doctor who tested positive at Princess Alexandra Hospital two weeks ago, but test results are not yet ready.
The female doctor had worked a shift at the hospital and visited four venues in the city's south the previous day.
Dr Young said at that time the number of people using check-in apps had helped contact-tracers quickly track down every person who had come into contact with the doctor.