He was reportedly killed trying to defend his girlfriend, singer and actress Kelly Khumalo.
The attack happened when men entered his girlfriend’s house in Vosloorus, south of Johannesburg.
His agent described him as a humble man from a tough background who had become a “hero in everyone’s eyes”.
The 27-year-old was the goalkeeper for Orlando Pirates and had captained Bafana Bafana in their last four matches in the African Nations Cup qualifiers without conceding a goal.
On Saturday, he was in action for his club, when they progressed to the semi-finals of the South African League Cup, beating Ajax Cape Town 4-1.
In a statement, the South African Police Service said two men had entered the house, around 20:00 (18:00 GMT), demanding mobiles phones and valuables. A third man remained outside.
All three fled on foot after shots were fired.
Meyiwa was declared dead on arrival at hospital.
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.”
Ephraim Mashaba, head coach of South Africa’s football team wept during a news conference called on Monday in response to the footballer’s death.
“Senzo was a very kind person,” he said. “I have never seen Senzo being sad or angry in the camp.”
Urging Meyiwa’s team-mates and colleagues to stay strong, he added: “Senzo is a team player, Senzo is everything.”
Meyiwa’s agent Mike Makaab called the death “a huge shock”, saying that Meyiwa was “really a hero in everybody’s eyes”.
Team mate Tsepo Masilela was among many voicing their shock at the news on social media.
“How do you kill someone for a cell phone?” he tweeted, saying the whole country was at a loss.
“When does it STOP South Africa?” wrote Darren Keet, the national team’s number two goalkeeper.
His girlfriend, Khumalo, Khumalo left her home in Vosloorus, on Monday.
Police had cordoned-off her home, along with a neighbouring house on either side.
Khumalo, dressed in a white shirt and jeans, with a light blue scarf wrapped around her head, drove out of her yard in a silver-grey BMW X6, accompanied by her younger sister.
She was escorted by police and drove past neighbours and media gathered near her home.