An ABF spokesperson said "all necessary contact tracing, quarantining, testing and deep cleaning" is underway.
"As a pre-cautionary measure all detainees at MITA will be offered COVID-19 testing," they said.
As of June this year there were 239 people living at the MITA facility, according to Department of Home Affairs data obtained by the Refugee Council of Australia.
It is unclear how many of those have been vaccinated, with the ABF saying "consenting detainees" had been offered the jab since a vaccine rollout began at the facility in early August.
"Health care services for detainees are generally commensurate with those available to the Australian community, under the Australian public health system and as clinically indicated and with the person's consent," the spokesperson said.
"The priority for the department/ABF is the health and safety of the detainees and staff."
It's not yet known how long the person was working at the Camp Road facility while infectious.
The Refugee Action Coalition said the infected worker was a Serco-contracted cleaner who had worked across all compounds inside the detention centre.
However, the ABF declined to comment on this and Serco directed all comment to the ABF.
"For privacy reasons, the department does not comment on individual cases," the ABF spokesperson said.
One MITA detainee, who did not want to be named, told the RAC they felt they "have just been left in the dark" about the outbreak.
"We asked which compounds have been exposed but Border Force would not tell us. They are just trying to cover things up," they said.
RAC spokesperson Ian Rintoul said access to COVID testing at the facility had been limited.
"Serco and Border Force are making up the rules as they go along, and it is always to the detriment of the detainees," he said.
"Playing fast and loose with COVID protocols is a high-risk game that is putting the health of potentially hundreds of vulnerable people in jeopardy.
"Border Force's lack of transparency is a risk to detainees and to the general community. The best way to keep detainees safe is to let them out. They are sitting ducks in detention."