Its carcass was recovered in the reserve late last week.
The horns of the third rhino were not removed, but investigators established that the animal had been shot and wounded in its shoulder and probably died a slow death after managing to escape from the poachers.
The hunt for the poachers is continuing amid gloomy reports that the toll of rhino poached countrywide this year has risen to 135 already.
The Kruger National Park has lost 75 rhino to poachers since the beginning of the year, department of environmental affairs spokesperson Albi Modise revealed this week. The second highest number of rhino slain by poachers is in KwaZulu-Natal with 18, Limpopo with 17 and the North West Province with 15.
The report said South Africa lost 448 rhino to illegal hunting and trade in rhino horn last year.
Modise said the department was encouraged by an increasing number of arrests and convictions this year to counter rhino poaching. He added that 89 people were arrested for illegal activities involving rhino horns across the country since January.
Colonel Vishnu Naidoo reported that a game reserve manager, Walter Nkuna, 40, who is believed to be linked to rhino poaching, shot and killed himself at Thabazimbi in Limpopo when police began to move in on him this week.