He is the fourth Australian to have died among the seven who are known to have caught the virus since it was first identified 15 years ago.
Dr Rodger's death follows little more than a year after the death of Brisbane veterinarian Ben Cunneen from the infection.
Dr Rodgers caught the infection while treating a sick horse at the J4S Equine Nursery at Cawarall, near Rockhampton nearly four weeks ago.
He believed at the time the horse was suffering from a snake bite and did not wear protective gear.
He opted for a five-day intravenous course of a drug called Ribavirin, normally used in the treatment of hepatitis. Doctors had hoped it would prevent the infection developing, but he was sick soon after the course had been completed.
Dr Rodgers had been in a coma at Princess Alexandra Hospital, in Brisbane. His condition had been critical throughout.
The Australian Veterinary Association said vets around Australia are mourning the death of Dr Rodgers.
It urged state and federal authorities to immediately increase investment in fighting the deadly disease.
"Just 12 months ago we lost friend and colleague Ben Cunneen to Hendra virus, a disease he contracted treating a sick horse, just as Alister did," said Dr Mark Lawrie, president of the association.
"It is absolutely devastating to lose another vet so soon, and we must do everything within our power to stop this from ever happening again.
"All indications are that Hendra is here to stay. It is probable that cases will emerge in states other than Queensland. Governments around Australia need to take this disease seriously right now and invest in measures to address the problem."
The association advocates a three-pronged approach to the Hendra response - education and training in preventive measures, research into a human cure, and better funding for government veterinary responses to outbreaks.
"We need some serious funding for education and training for everyone involved with horses, including owners and veterinarians, about how to lower the risk of falling victim to Hendra.
"Even the most stringent preventive measures are not foolproof, however, and it's vital that some progress is made immediately on treating the disease once a person has been exposed. We need a massive research effort into the source of the disease, vaccines and rapid onsite tests.
"Our third concern is that Australian government veterinary services have been progressively starved of resources over many years. We need access to quick lab results, and enough government vets to respond to outbreaks of disease wherever they are.
"It's likely that with greater awareness of the disease, the number of suspected cases will increase. To avoid any more deaths, we need urgent action in all three areas," Dr Lawrie said.
"We extend the sympathy of veterinarians around the country to Alister's family, friends and workmates," Dr Lawrie said.
The Hendra virus is carried by Australian fruit bats. It is passed on to horses in rare instances, most likely through contact with bat urine, faeces or other bodily fluids.
It is possible for people to catch the virus from horses.
There have been no known cases of person to person transmission, or bat to person transmission, although authorities suggest people refrain from handling bats.