Lieutenant-General Solomon Makgale said Meyiwa was shot at his girlfriend's house in Vosloorus, a township about 20 kilometres south of the city, and declared dead on admission to hospital.
A South Africa police official said two men entered the house of Kelly Khumalo, who is a local actress and singer.
"Two guys entered the house and demanded cellphones, money and other valuables," provincial Community Safety official Sizakele Nkosi-Malubane said.
"Senzo tried to protect Kelly because one of the men had a gun pointed towards her."
The intruders fled, along with a third man who had been waiting outside. Other people in the house were unharmed.
Meyiwa played for the Orlando Pirates on Saturday and has represented the national team in their past four 2015 Africa Cup qualifiers.
The cause of the 27-year-old's death was not given by the club, but the South African Police Service (SAPS) tweeted: "We have to break normal protocol. We can confirm that Bucs keeper Senzo Meyiwa has been shot and sadly declared dead on arrival at hospital."
The Pirates, for who Meyiwa played on Saturday, said: "The @Orlando--Pirates family has learned with sadness of the untimely death of our number 1 keeper & captain Senzo Meyiwa."
Club chairman Dr Irvin Khoza added: "This is a sad loss to Senzo's family especially his children, to Orlando Pirates & the nation."
Having made his debut for Orlando in 2005, Meyiwa had made his mark for the South African national team in 2014, captaining the side in their last four qualifiers for the African Nations Cup.
International team-mates Dean Furman and Andile Jali reacted to the news on Twitter.
Furman, who plays for Doncaster player, said: "Beyond devastated at the loss of our captain & friend Senzo Meyiwa. Thoughts & prayers are with his family & friends at this terrible time."
Jali, who moved from Pirates to Belgium club Ostend this year, added: "Just got a call and I was sleeping, but now I cannot sleep because of what I just heard."
Orlando Pirates are planning to give a press conference on Monday.
The death of the national football team captain is the second tragedy to hit South African sport within three days after former world 800m athletics champion Mbulaeni Mulaudzi died on Friday in a car crash.
