Inspector Wilmarie van der Merwe said the girls were left alone at home in Magogoe village near Mmabatho on Sunday while their mother attended a funeral.
They cooked a pot of porridge for lunch and ate it with a can of fish. They then went to play outside and ate the leftovers in the evening.
At around 2am on Monday, the toddler complained of a sore stomach and her sister soon developed the same symptoms.
The three-year-old threw up until she lost consciousness. Both girls were taken to the Mafikeng provincial hospital where the younger one was declared dead on arrival.
Her sister was in a stable condition in hospital.
Van der Merwe said police have opened an inquest into the death of the three-year-old and an autopsy would be conducted to determine the cause of her death.
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