The treatment had the potential to stop the disease developing, experts believe, but has never been tried on anyone possibly exposed to the virus.
Queensland chief health officer Jeannette Young said those who took up the offer would need to be admitted to Rockhampton Hospital and receive an infusion of the drug for five days.
The drug, ribavirin, is normally used in hepatitis treatment.
It is understood treatment would have to begin soon as the incubation period ranges from just five days to two weeks.
Queensland Health has tested a total of 13 people for the virus, but initial testing may not yield a reliable result during the incubation period.
Of those, the four considered most seriously exposed - two of whom were sprayed with blood and mucus from the horses that died on the virus on Saturday - have been offered the new treatment.
Meanwhile, another horse on the property, the J4S Equine Nursery at Cawarral, east of Rockhampton, recorded a raised temperature yesterday and veterinary authorities confirmed it was higher again today.
All horses on the property are being closely monitored.
The results of the initial round of testing of all horses on the property will be known tomorrow. Any horses testing positive will be euthanized.
In all, 42 horses are known to have contracted Hendra since the virus was first identified. Six cases have resulted in people, half of which proved fatal.
The most recent fatality was Brisbane veterinarian Ben Cunneen, who died almost a year ago after an outbreak at a Redlands veterinary clinic.