The Spanish driver said in a video message on 27 February that he was "completely fine", suggesting he would be ready for the Australian GP.
However, the club have now made an official announcement to confirm that even though the Spanish driver is "entirely healthy from neurological and cardiac" issues, he will not be able to compete in the first race of the season, leaving Kevin Magnussen to take his place in the line-up.
"Having performed an exhaustive series of tests and scans – some of them as recently as yesterday evening – McLaren-Honda driver Fernando Alonso's doctors have informed him that they find him asymptomatic of any medical issue; that they see no evidence whatsoever of any injury; and that they therefore describe him as entirely healthy from neurological and cardiac perspectives alike," the team said.
"However, Fernando's doctors have recommended to him that, following the concussion he sustained in a testing accident at the Circuit de Barcelona-Catalunya on February 22, 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 so soon after his previous one, so as to minimise the chances of second impact syndrome, as is normal medical procedure when treating athletes after concussions."
"In order to limit those environmental risk factors, specifically, his doctors have advised that he should not compete in the imminent Australian Grand Prix meeting, which will take place on March 13, 14 and 15.
"Fernando has understood and accepted that advice, and the two McLaren-Honda cars will therefore be driven in Australia by Fernando's team-mate Jenson Button and the team's test and reserve driver Kevin Magnussen."
Following recommendations from the doctors, the McLaren-Honda team hope Alonso will be ready to drive in Malaysia.
The team added: "Fernando's doctors acknowledge that he feels fit and well, and that he regards himself as ready to race, and, that being the case, 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 meeting on March 27, 28 and 29.
"Indeed, his doctors are supportive of that ambition, satisfied as they are that he sustained no damage whatsoever during his testing accident on February 22. All at McLaren-Honda fully support Fernando's decision in respect of his doctors' advice."