In a statement on Monday, Mr Andrews announced he tested positive from a rapid antigen swab after developing mild symptoms including a sore throat and mild temperature.
He will isolate with his family for the next seven days, with James Merlino to serve as acting premier until 4 April.
The news comes as Australia recorded three new COVID-19 deaths on Monday and the federal and ACT governments signed an agreement to invest $38 million in mental health and suicide prevention as part of the territory's pandemic recovery.
NSW reported three COVID-19 deaths and 16,199 new infections, down from 17,450 on Sunday.
There are currently 1,270 patients in hospital across the state — up from 1,171 on Sunday — with 55 in intensive care.
In Victoria, the health department reported 8,739 new infections, taking the total number of active cases in the state to 56,997.
Of those cases, 252 patients are in hospital, 21 in ICU and six on ventilators.
The numbers come as the federal and ACT governments agreed to invest $38 million in mental health and suicide prevention as part of the territory's pandemic recovery.
Under the deal, the Commonwealth will spend $25.2 million and the ACT $12.9 million over the next five years.
Federal Health Minister Greg Hunt said the agreement will ensure ACT residents have access to support when and where they need it.
"This landmark agreement will be of immense benefit to everyone in the ACT and will support our ongoing national recovery from the impacts of the COVID-19 pandemic," he said on Sunday.
ACT Chief Minister Andrew Barr particularly welcomed additional investment in early intervention and prevention as a part of the nation's approach to addressing mental illness.
Hundreds of Tasmanians get wrong virus message
Meanwhile Tasmania's health department has apologised for sending messages to 540 people with coronavirus that wrongly told them they were close contacts.
The state health department said the error occurred on Saturday and was "corrected immediately".
"540 people incorrectly received messages notifying them they were close contacts for COVID-19, when they should have received messages advising them of their requirements to isolate as a case of COVID-19," acting State Health Commander Dale Webster said in a statement.
"These people were already identified as cases having either registered a positive RAT or receiving a notification from the laboratory of their positive result."
Mr Webster said follow-up messages advised the people of the mistake and of their isolation requirements.
"On behalf of the department of health, I apologise for the error and for any inconvenience caused to the recipients of the incorrect messages," he said.
Mr Webster said processes are subjected to a continual internal review.
Last week, 19 Tasmanians who tested positive were incorrectly informed they had tested negative. The health department said the error was corrected within three hours.
The island state recorded 1,726 new cases on Monday, an increase of 209 from Sunday, taking the number of active infections to 10,939.
There are 27 people with the virus in hospital. None are in intensive care.
