According to initial reports in local media, model Reeva Steenkamp, 30, may have been mistaken for a burglar at the property in the Silver Lakes Golf Estate in Pretoria.
But police said the shooting early today was being treated as a murder investigation and said there had been previous incidents at the address described as “allegations of a domestic nature”.
Brigadier Denise Beukes also said police were “very surprised” by the burglar suggestion, telling reporters near the scene: “These allegations did not come from us.”
Brigadier Beukes said Pistorius will be appearing in court this afternoon and bringing a formal bail application.
Confirming there had been previous “incidents” at the athlete’s home, she said: “I can’t confirm that it’s related to the person that’s arrested but I can confirm there has previously been incidents at the home of Mr Oscar Pistorius.”
She said these were “allegations of a domestic nature”.
She said there was no signs of forced entry at the address.
And asked about speculation the victim may have been mistaken for a burglar, she said: “The South African Police Service were just as surprised this morning to hear over the radio that allegations had been made that the deceased had been perceived to be a burglar.
“We were very surprised and those allegations did not come from us.”
The officer said Pistorius was co-operating with police.
There had been speculation the shooting may have been a Valentine’s Day surprise gone wrong. Miss Steenkamp, described in her Twitter biography as a model, cover girl and law graduate, had tweeted about Valentine’s Day yesterday, writing: “What do you have up your sleeve for your love tomorrow??? #getexcited #ValentinesDay”.
Pistorius, 26, appeared to have serious concerns about his safety and was said to sleep with a revolver by his side.
A journalist from the Daily Mail who interviewed Pistorius last summer noted: “This being South Africa, one baseball bat and one cricket bat lie behind Pistorius’s bedroom door. A revolver is at his bedside. A machine gun by his window.”
Pistorius’s father said his son was “sad” following the shooting.
Henke Pistorius told SABC radio news: “I don’t know nothing. It will be extremely obnoxious and rude to speculate. I don’t know the facts.
“If anyone makes a statement, it will have to be Oscar. He’s sad at the moment.”
Police spokeswoman Lt Col Katlego Mogale told the South African Press Association police were called to Pistorius’s home early today.
She said: “Paramedics declared the woman dead on the scene and police proceeded with their investigation. The woman sustained wounds to her head and the upper body.”
A 9mm pistol was recovered. According to unconfirmed reports four shots were fired.
Gold medal winner Pistorius is known as the Blade Runner because of the ground-breaking prosthetics he uses for racing.
He made history at the London 2012 Olympics when he became the first amputee sprinter to compete in the able-bodied Games, running in the 400m and 4x400m relay.
The Johannesburg-born athlete, who was born without fibulas in his legs and had the limbs amputated below the knee when he was 11 months old, had to win a legal battle over his blades with the International Association of Athletics Federations (IAAF) in 2008 for the right to compete in able-bodied competition.
Miss Steenkamp’s publicist Sarit Tomlinson paid tribute to Steenkamp, describing her as “the sweetest human being and an absolute angel on earth”. She added: “She was the kindest, most unbelievable girl.”
She told Sky News: “It’s shocking. No one knows what happened. We’re waiting for information. There are people we are waiting to speak to, to validate some of the stories.”
She described Steenkamp as a “rising star”.
“There was so much in the pipeline for her,” said Ms Tomlinson. “She was just about to explode into the media. A very talented, very bright young girl. It’s a huge loss for everyone. It’s just too shocking for words.”
Asked how much she would miss Steenkamp, she added: “There’s no words to describe how much. Our condolences to her family, because for her family it’s all about them right now.”
Asked about Steenkamp’s relationship with Pistorius, Ms Tomlinson said: “They had been together for a couple of months and it’s been a fabulous relationship - a healthy, fabulous relationship.”
Tropika Island of Treasure - an entertainment show starring Miss Steenkamp due to be broadcast this weekend - posted a tribute to her on its website.
It says: “We are deeply saddened and extend our condolences to Reeva’s family and friends.”
Athletes joined fans in paying tribute to Miss Steenkamp.
Jessica Ennis spoke of her shock on Twitter, describing the “the horrendous news” as “an awful tragedy”.
Denise Lewis added: “Not a good morning athletics fans - News reports on Oscar Pistorius are unbelievable”.
Less than 24 hours ago, Pistorius was active on his Twitter account, retweeting South African movie channel MNet.
The tweet was about a film the channel is showing as part of its Oscars film awards celebrations - a campaign Pistorius is a brand ambassador for, according to his website.
Just three days ago, Pistorius tweeted about his excitement regarding his first race of 2013, accompanied by a photograph of him in action.
He said: “1 month till my first race of 2013.. Can’t wait to burn it up!”
On Pistorius’s website, a quote from Lord Coe written before London 2012 describes him as a “real inspiration to people around the world”, and a spokesman from sports giant Nike describes time with Pistorius as “some of the most inspirational time we’ve ever spent around an athlete”.
Lord Coe said: “Oscar is an extraordinary athlete who has made a significant impact in international sport.
“It will be fantastic to see him compete in London this summer - spectators can expect a real treat!
“He’s been a real inspiration to people around the world so we were thrilled when he decided to join our International Inspiration programme as an ambassador, helping us to inspire young people worldwide.”
London 2012 Paralympic 200m champion Richard Whitehead tweeted: “Shocking news this morning regards my buddy Oscar P what a tragedy!!! Unbelievable I’m speechless #oscar.”
Britain’s Paralympic discus champions also went online to relay their shock.
Aled Davies tweeted “wow... Crazy news about Oscar... Devastating and speechless...” while Josie Pearson simply stated it was “Tragic...”
Wheelchair racer Shelly Woods, silver medallist in the London 2012 Paralympic marathon, tweeted: “Woke up to shocking news about Oscar Pistorius, very very sad...”