The 22-year-old woman and the child died on Sunday morning, provincial commissioner Lieutenant General Fannie Masemola said in a statement.
The man allegedly went to his girlfriend’s house in Regorogile Extension, Thabazimbi, and demanded to see her.
When she refused to, the man allegedly forced the door open, dragged her outside and started hitting her with stones — which left her unconscious, Masemola said.
The man then set the woman’s house on fire burning the child, who was in the house, alive. He then fled the scene.
Masemola urged the community to assist the police in finding the man.
Meanwhile in a separate incident on Friday, a 20-year-old man from Ha-Mashau just outside Levubu, shot and killed his girlfriend and her mother.
The 19-year-old youth and her boyfriend had had an argument, Masemola said.
The man then allegedly stole a gun belonging to his grandfather from his car and shot the two at their home. He then fled the scene.
“A manhunt was launched and the suspect was arrested on Saturday morning after he retreated to his home,” Masemola said.
The man would appear at the Levubu Magistrate’s Court on Monday. He was charged with two counts of murder and one of theft.
His 68-year-old grandfather was charged with negligent handling of a firearm according to the Firearms Control Act, Masemola said.