And it is a blow for the NRL's anti-vaccination players including Manly duo Dylan Walker and Addin Fonua-Blake, Canterbury rake Sione Katoa plus Canberra trio Josh Papalii, Sia Soliola and Joseph Tapine.
It is believed a total of about 20 players have signed a waiver to avoid a flu jab for various reasons.
ARL Commission chairman Peter V'landys had been confident the Queensland government would accept their biosecurity guidelines that would allow NRL players to sign a waiver to refuse the vaccination.
It would have cleared Cartwright and Kelly to return to training after they were sidelined following the Queensland government's intervention.
But Dr Young said she had told the NRL they would only provide exemptions for players who have had adverse reactions to vaccinations.
"I sent a letter to the NRL yesterday in which I did exempt them for medical contrary indications," she said.
"If they have got medical reasons for not being vaccinated (they will receive an exemption).
"If they have had an anaphylactic reaction to previous flu vaccine or any component of a flu vaccine, you do not need to be vaccinated so I have provided that exemption."
Asked if players could receive an exemption on any other grounds, Dr Young said: "That's not covered.
"Although the NRL did not put that in their initial submission to me I thought it was reasonable that the NRL players, support staff, coaches and officials have that same exemption that I provide for visitors going into aged-care facilities or for children."
Cartwright and Kelly are the only NRL players to have been stood down after the NSW government refused to adopt Queensland's "no jab, no play" stance.
However, a number of interstate NRL players won't be allowed to play when their teams visit Queensland after the competition restart due to the state government's policy.
The NRL said they accepted the Queensland government's call.
"We respect the decision of the Queensland Chief Health Officer and are working with clubs to mitigate the impact on the season when it resumes on May 28," a spokesman said.
"We have always said we will comply with the directions of relevant government and health authorities.
"It will mean a small number of players will be ineligible to play in Queensland while the current restrictions remain in place."
Danny Levi said it would be a blow if Manly teammates Walker and Fonua-Blake were not allowed to play in Queensland.
"Obviously it would be pretty disappointing," he said.
"But at the same time the game is trying to make sure everyone is healthy, and as long as I am keeping myself fit and healthy that's all I can worry about."
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