A helicopter, ambulances and other emergency vehicles rushed to the scene as guards struggled to impose order at St Albans prison, which was also hit by a deadly riot in 2013.
Officials declined to say whether the three fatalities were prisoners or guards, but added that investigations were under way and Justice Minister Michael Masutha would visit the prison on Tuesday.
"There was a clash between prison officials and inmates resulting in the deaths of three people and 26 others injured," Correctional Services spokesman Logan Maistry told AFP.
Ten of the injured were in a serious condition in hospital.
Maistry said that special security measures are put in place each year over the holiday period to tackle any protests or unrest in prisons.
Local media reported that the prison was put on lockdown, with many visitors turned away when they arrived to see relatives.
The prison in Eastern Cape province has a history of attacks by inmates on wardens.
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