Dr Alister Rodgers is in an induced coma in Princess Alexandra Hospital, having been the sevneth person known to have contracted the virus since it was identified in 1994.
He contracted the virus while treating a horse dying from the rare infection at the J4S Equine Nursery at Cawarall, near Rockhampton.
A statement by Linda, Courtney and Duncan Rodgers spoke of their immense gratitude "to every person who has supported Alister and our family during his illness".
They continued: "Alister would be deeply touched. The response has been overwhelming and has come from friends, acquaintances and even strangers," the statement said.
"The people of Rockhampton - especially his colleagues at Rockhampton Veterinary Clinic, those who cared for him at Rockhampton Hospital and many veterinary colleagues - will always remain special to us.
"Our thoughts are also with those people and their loved ones who are waiting for test results and care for any serious condition," they said in reference to staff at the stud potentially exposed to the virus, including three under observation at Princess Alexandra Hospital.
"They are no less deserving of our thoughts. The task for Queensland Health in juggling the huge demands from all quarters of the community is more than substantial.
"The workers there need support and thanks too.
"For most of the last 48 hours, we have been preoccupied with the seriousness of Alister's condition.
"But we have been concerned and distressed also about claims that Alister should not have been released from Rockhampton Hospital after completing a trial course of anti-viral medication.
"Alister showed no symptoms that are distinctive of Hendra Virus when he was discharged, although he understandably remained anxious - as anyone would in such a situation.
"Based upon the previous pathology of this virus, he was thought to be 'safe'.
"Those who have cared for him and have fought for his life should not be condemned for this.
"It has been important for us to maintain our privacy throughout this ordeal.
"We have enough to deal with for now and in the immediate future.
"But the importance of our sincere gratitude and thoughts cannot be left unsaid."
Dr Rodgers runs the Rockhampton Veterinary Clinic and Rockhampton Equine Clinic.
Princess Alexandra Hospital, in a statement released this week, said all patients admitted in relation to Hendra virus had requested privacy and no further statements regarding their condition would be provided by hospital staff.