The animal, described as a cross between a red deer and an elk, had been kept by the couple as a pet for about 6 years.
Paul McDonald, 46, had gone out to feed the animal in the morning on the property at Moyhu in Victoria state when he was attacked, according to Police Sergeant Paul Pursell.
"His wife and son heard the commotion and went out to see what was going on," Pursell told reporters. "His wife entered the enclosure to assist her husband and she was also attacked."
The couple's teenage son then struck the deer with a lump of wood to save his mother, the Australian Broadcasting Corporation reported.
Officers were called to the property and shot the deer before a paramedic treated the couple.
Paul McDonald, who was gored by the animal, died at the scene, according to the BBC.
His wife, Mandi McDonald, was flown by helicopter to the Alfred Hospital in Melbourne where her condition was described as critical. She was being treated for upper body and leg injuries, according to Sky News.
"The family is just devastated," Pursell said. "It's beyond words how they've been affected by this incident today."
While deer attacks are almost unheard of in Australia, Pursell warned that deer behavior could be unpredictable.
David Voss, president of the Australian Deer Association, a hunting and deer management organization, said farmed deer tend to be more aggressive than wild deer, but he had only heard of similar attacks "very occasionally."
Deer were introduced to Australia by British settlers in the 19th century and have established wild populations.
The Associated Press contributed to this report.