Tweefontein police spokesperson Inspector Patrick Mabena said the crime was committed in Section C on Saturday afternoon.
He said the mother of the child, a woman in her mid-30s, was cooking in the kitchen when she heard her daughter crying in the bedroom.
"The woman went to investigate and found the toddler lying on the bed, with the boy standing next to it," Mabena said.
"When she asked him what had happened to her child, the teenager allegedly told his stepmother that he raped her in revenge."
The teenager was apparently angry at his stepmother because she had accused him of stealing money from the house.
Mabena said the child was taken to a clinic where it was confirmed that she had been raped.
The teenager was expected to appear at the KwaMhlanga Magistrate's Court soon.