Major hunt for killers of S. Africa footballer Senzo Meyiwa
They have offered a reward of 250,000 rand (£14,000; $23,000) for information about the attack, which highlights the country's high rates of violent crime.
Meyiwa, 27, was reportedly shot after men entered his girlfriend's house.
President Jacob Zuma led tributes to the goalkeeper, saying “words cannot express the nation's shock”.
Police said two men had entered the house in Vosloorus, south of Johannesburg, at around 20:00 (18:00 GMT), demanding mobile phones and valuables. A third man remained outside.
One of the two was described by police as tall, dark-skinned and slender with dreadlocks, and the other was said to be short, dark-skinned and well-built.
Meyiwa was reportedly shot at the house of singer and actress Kelly Khumalo, who was his girlfriend
President Jacob Zuma, pictured here with Meyiwa in 2013, said words could not express the nation's shock
National Police Commissioner Riah Phiyega told a press conference that Meyiwa was shot once in the upper body as he moved towards the door. The three men then fled on foot, she said.
The footballer was declared dead on arrival at hospital.
Relatives and fans gathered at the hospital and at the crime scene outside the home of well-known singer and actress Kelly Khumalo, who Meyiwa had been dating.
South African President Jacob Zuma said in a statement on Monday: “We mourn the death of this young footballer and team leader whose life has been taken away at the prime of his career. Words cannot express the nation's shock at this loss.”
Police say Senzo Meyiwa was shot during a robbery whilst visiting friends
The whole nation is mourning the passing of a national football hero. Radio and TV chat shows are clogged with callers expressing their shock and dismay.
His shooting brings into sharp focus the wider issues of gun crime in South Africa, particularly so soon after the trial of athlete Oscar Pistorius, who says he shot dead his girlfriend by mistake, fearing there was an intruder in the house.
South Africa is asking itself deep questions about the cancer of violence that has killed some of its best talent. It was seven years ago this month that renowned reggae singer Lucky Dube was killed in a robbery. The question in many people's minds is: there is crime all over the world, but why is it that here in South Africa violence is so gratuitous?
Who was Senzo Meyiwa?
Senzo Meyiwa began playing for Orlando Pirates in 2005 and went on to captain the national team
Born on 24 September 1987
Goalkeeper for Johannesburg club Orlando Pirates
Made his international debut in June 2013
Appointed South Africa captain in September 2014
Seven international caps
Actress Kelly Khumalo was girlfriend
Had a child with her
Meyiwa was 'one of the best goalkeepers in Africa'
'Senzo is everything'
Ephraim Mashaba, head coach of South Africa's football team, wept during a news conference on Monday, telling reporters: “Senzo is a team player, Senzo is everything.”
His words were echoed by South Africa midfielder Dean Furman who told the BBC that Meyiwa was “just the nicest guy you could wish to meet”.
The player's agent, Mike Makaab, called the death “a huge shock” and said Meyiwa was “really a hero in everybody's eyes”.
The South African football league has cancelled next weekend's derby between his club, Orlando Pirates, and their rivals Kaiser Chiefs as a mark of respect.
Investigators worked outside the scene of the shooting in the Vosloorus township on Monday
His death is the second blow to South Africa's sporting community in three days. On Friday, former 800m world champion runner Mbulaeni Mulaudzi was killed in a car crash.
The shooting has once again highlighted South Africa's high crime rates and problems with gun violence.
Between April 2013 and March 2014, more than 17,000 people were murdered in South Africa, an increase of about 5% since the previous year, according to police figures.