The Orlando Pirates goalkeeper was killed after being shot on Sunday when he reportedly attempted to protect his girlfriend after intruders broke into her property in Vosloorus on the outskirts of Johannesburg.
South African president Jacob Zuma called for those responsible to be brought to justice as the nation mourns Meyiwa's passing.
Speaking at a press conference on Monday, an emotional national team coach Ephraim Mashaba described the 27-year-old as a "peacemaker" and said his spirit will "live forever".
Pirates chairman Dr Irvin Khoza said Meyiwa, who also skippered his club, had put his club on the map and left a legacy, while Saturday's derby clash against Kaiser Chiefs in the ABSA Premiership has been called off as a mark of respect for the deceased.
Meanwhile, FIFA president Sepp Blatter tweeted: "Thoughts with family, players & fans of @Orlando_Pirates & @BafanaBafana. A senseless, tragic loss. #RIPSenzoMeyiwa."
Confederation of African Football (CAF) president Issa Hayatou has also expressed his grief following the sad news of Meyiwa's death.
In a letter to South African Football Association (SAFA) president Danny Jordaan, Hayatou said: "It is with shock and dismay that CAF has learnt about the passing away of South Africa and Orlando Pirates captain and goalkeeper Senzo Meyiwa.
"Losing such a talented player and young gentlemen is a tragedy for South African and African football, and our thoughts are with his family and relatives.
"Meyiwa was one of the most promising South African players and he took with great pride and responsibility his role as captain of both the national team and his club Orlando Pirates. Words cannot express enough our sadness.
"In my personal name, on behalf of the CAF Executive Committee and the entire African football family, we present to the family of the deceased, to SAFA, to Orlando Pirates and to all those who knew Meyiwa our deepest condolences."
Legendary former South Africa captain Lucas Radebe tweeted: "Tragic news abt [sic] the passing of @orlandopirates @BafanaBafana captain. Sad sad news don't know wat to say......"
A Bafana Bafana team-mate of Meyiwa's, Dean Furman, tweeted: "Beyond devastated at the loss of our captain & friend Senzo Meyiwa. Thoughts and prayers are with his family and friends at this terrible time."
The South African Sports Confederation and Olympic Committee (SASCOC) mourned the passing of a second top South African sportsman in the space of three days, after Olympic 800 metres runner Mbulaeni Mulaudzi died in a car crash on Friday.
"The South African sporting world is deeply shocked at this latest news," said SASCOC CEO Tubby Reddy.
"To lose two sporting icons such as these gentlemen in the space of just a few days has rocked the very fibre of the national sports family. Our hearts go out to Senzo Meyiwa's family, friends as well as his footballing team-mates."
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