Paralympian Oscar Pistorius will spend the night behind bars and appear in the Pretoria Magistrate's Court on a charge of murder on Friday, the National Prosecuting Authority (NPA) said.
"He will be kept in police custody," NPA spokesperson Medupe Simasiku said on Thursday.
Pistorius's girlfriend Reeva Steenkamp, who was a model and law graduate, was shot dead in his home in the early hours on Thursday.
Brigadier Denise Beukes has not named Pistorius as the person arrested, as he has yet to appear in court, and has instead referred only to "a 26-year-old".
She said the court had indicated it could not run a bail application on Thursday afternoon.
Steenkamp was killed in Pistorius's home in Silver Woods country estate, in Pretoria, which is accessible through booms and a security check.
At first it was reported that he had mistaken her for a burglar.
Talk shows and social media speculated about what could have happened, and what the appropriate action should be in terms of gun laws.
Police later said this information did not come from them.
Beukes told reporters there had been "incidents" at Pistorius's house.
"I confirm there had been previous incidents of a domestic nature at his place, but this will form part of the investigation," she said.
As the world's media reported on the tragedy, M-Net became the first to break commercial ties with him, announcing that it had withdrawn its campaign with him promoting the Academy Awards.
On her Facebook profile page, Steenkamp described herself as an "SA Model, FHM Cover Girl, Tropika Island of Treasure Celeb Contestant, Law Graduate, Ambassador".
She had just featured in a lingerie shoot in the Valentine's issue of Heat magazine, and one of the last posts on her Facebook page expressed concern about the rape and murder of Anene Booysen in Bredasdorp.
Her Twitter feed was filled with messages of support to friends and notes about the promotions in which she was involved.
Hours before her death, she posted the Valentine's Day tweet: "What do you have up your sleeve for your love tomorrow???".
Sarit Tomlinson, MD of Capacity Relations, which managed her publicity, said in a statement: "We can confirm that Reeva Steenkamp has passed away... Our thoughts and prayers go to the Steenkamp family, who have asked to have their privacy respected during this difficult time; everyone is simply devastated.
"She was the kindest, sweetest human being; an angel on earth who will be sorely missed."
On Thursday morning, Pistorius was driven in a convoy from his home to the Boschkop police station, then to the Mamelodi Day Clinic for a routine medical examination and taking of samples, then back to the police station.
Outside his home, Steenkamp's model friend Mashadi Motsogi was in tears.
She had seen on Twitter that Steenkamp had been shot, but did not believe it until she saw journalists outside the estate.
"I know Oscar stays here. When I called here, he did not reply. He did not answer my call."
She described Steenkamp as a "friendly person, always willing to help other people".
"She never snapped," said Motsogi, who had looked to Steenkamp, an established model, for advice.
"I have lost a friend," she said, tears streaming down her face.
Reporters were kept at bay while police forensics experts worked at the scene.
Domestic workers leaving at the end of the day described the situation inside the estate as being "quiet, but tense".
"No one is speaking... about the incident. People are afraid to talk. We heard about it in the news. Our employers are not talking to us about it," said Dimakotso Moetje.
"We are shocked and disappointed. We loved Oscar. We look at him as a role model for our children."
Another domestic worker, Maggy Selepe, said she was shocked when her employer called her with the news.
"We switched on the television and there... [was] the news about Oscar. I was shocked and disappointed. I don't know how it happened, but here we are, something horrible happened in this complex."