The former world number one was to go to Australia on one of the 18 charter flights set up by the tournament organizers but is still isolating himself at home.
Sir Andy is believed to be in good health despite the infection.
The tournament – the first Grand Slam of the year – doesn’t start until February 8 and Murray hopes to travel at a later date.
Tournament organizers have spent months negotiating with authorities to allow more than 1,000 players and staff to enter Australia.
Players are expected to start arriving within the next 24 hours.
They will then be quarantined for two weeks, during which they will be allowed out of their rooms to practice five hours a day.
Three-time Grand Slam winner, Murray is a five-time finalist at the Melbourne event and received a wild card entry for that year.
In the days leading up to the 2019 competition, he cried at a press conference after saying he feared the tournament would be the last of his career as he struggled to recover from surgery at the hip.
The 33-year-old former Wimbledon champion, however, continued to try to get back in shape.
He made his Grand Slam comeback at the US Open and French Open last year, but was knocked out in the opening rounds and is currently 123rd in the world rankings.
Sir Andy joins a list of tennis stars who have had the virus, including Novak Djokovic and Grigor Dimitrov.