The double world champion was concussed and airlifted to hospital
after losing control of his McLaren at the penultimate winter test in Barcelona last month.
The Spaniard is now recovering at home
but doctors have indicated returning to racing in Melbourne three weeks after after the high impact could be too risky.
Alonso commented on Twitter: "It will be tough not to be in Australia, but I understand the recommendations. A second impact in less than 21 days "NO".
McLaren explained in a statement: "Fernando's doctors have recommended to him that, following the concussion he sustained on February 22nd, for the time being he should seek to limit as far as is possible any environmental risk factors that could potentially result in his sustaining another concussion."
Kevin Magnussen -- who effectively lost his seat to Alonso when the Spaniard returned to McLaren after his Ferrari exit -- will race alongside Jenson Button in the Australian Grand Prix on March 15th.
Alonso's return to the starting grid in McLaren colors has been delayed by his freakish crash at the Circuit de Catalunya, home to the Spanish Grand Prix.
McLaren had explained that Alonso's "accident was caused by the unpredictably gusty winds at that part of the circuit at that time."
Turn Three, where the accident took place, is an area of the circuit where cross winds are known to affect the balance of the cars.
The 33-year-old posted a video on social media on Friday to thank his fans for his support and update them on his condition.
Standing in a garden, a smiling Alonso said: "As you can see I'm completely fine. I will rest and keep you updated next week with progress and see you very soon on the track."
But his return to the racing asphalt has now been delayed until at least the Malaysian Grand Prix at the end of March despite doctors saying he has no symptoms of illness.
"Having performed an exhaustive series of tests and scans -- some of them as recently as yesterday evening -- Alonso's doctors have informed him that they find him asymptomatic of any medical issue; that they see no evidence whatsoever of any injury," McLaren said in a statement.
"They therefore describe him as entirely healthy from neurological and cardiac perspectives alike."
However, in order to limit the risk of a secondary concussion Alonso has accepted the advice not to race but has continued his preparations for the new F1 season.
"Fernando's doctors acknowledge that he feels fit and well, and that he regards himself as ready to race," the statement continued.
"They are comfortable with the fact that he has already recommenced physical training, with a view to preparing for a return to the cockpit of his McLaren-Honda car for the Malaysian Grand Prix. Indeed, his doctors are supportive of that ambition."
Alonso chose to leave Ferrari
at the end of the 2014 season and rejoin McLaren, which is also renewing its technical partnership with Japanese engine manufacturer Honda for 2015.
The Spaniard -- regarded by his peers as the best driver on the grid -- is chasing a third world crown but, so far, he has not had chance to gauge the possibilities of realizing that ambition with McLaren.
Early reliability problems meant Alonso had only completed 117 laps in the MP4-30 race car before his preseason was curtailed by the crash.