The 27-year-old man handed himself over at the Gugulethu police station in Cape Town on Saturday "when he realised police were hot on his heels", said Brigadier Novela Potelwa.
The man, whose identity is known to News24, cannot be named until he has appeared in court.
Potelwa said the man had been on the run since the shooting of Sabsana, aged 28, last Monday.
He faced a slew of other criminal cases against him, according to the police.
At the time of the murder, he was out on bail in connection with a house robbery in Gugulethu.
He was also due in court the day after the murder, last Tuesday, in connection with a domestic violence case involving Sabsana.
Last Wednesday, he was due in court for an assault case.
He will now appear in the Athlone Magistrate's court on Monday on charges of murder.
Detectives will oppose bail.
In the tragic case, Sabsana, who was a successful business owner, was shot at her home in Gugulethu in front of her parents and son, aged 10.
In an interview with her parents, detailed in an article by City Vision on the News24 website, they said that the man shot their daughter as she arrived home.
She collapsed in the passage and he then walked to his car and drove off.
She was rushed to hospital, but died on arrival.
