The World Cup has opened amid jubilant scenes in South Africa, but Nelson Mandela missed the event after a car crash killed his great-granddaughter.
Zenani Mandela, 13, died when the car taking her home from a pre-competition concert in Soweto overturned.
The car's driver was arrested and charged with drink-driving.
The Nelson Mandela Foundation said the tragedy made it inappropriate for the former president, who is 91, to attend the opening ceremony in Johannesburg.
"We are sure that South Africans and people all over the world will stand in solidarity with Mr Mandela and his family in the aftermath of this tragedy," said a statement.
"We continue to believe that the World Cup is a momentous and historic occasion for South Africa and the continent and we are certain it will be a huge success.
"Madiba [Mr Mandela's clan name] will be there with you in spirit today."
A host of celebrities from the world of politics, business and sport attended a vibrant opening ceremony at Soweto's Soccer City stadium.
More than 1,500 performers took part in the event, which was broadcast in 200 countries.
Crowds of flag-draped sporting fans had flocked to the venue accompanied by the cacophony of vuvuzelas (traditional African trumpets).
But the celebratory mood was definitely tainted by the Mandela family tragedy, says the BBC's Karen Allen in Johannesburg.
Addressing the 94,000-strong crowd before the competition's opening game between South Africa and Mexico, Fifa President Sepp Blatter said: "A dream came true tonight and even if he is not here the spirit of Mandela is in Soccer City."
Before officially opening the competition, South African President Jacob Zuma said: "The nation shares your loss and mourns with you, especially on the day on which our dreams and hopes come alive."
The car carrying Zenani Mandela overturned as it came off a slip road on the M1 motorway, which travels through Johannesburg city centre, at about 0030 local time (2230 GMT on Thursday), reports said.
The male driver, who was reportedly unhurt and has not yet been named, may also face culpable homicide charges, police said.
"He lost control of the vehicle and it collided with a barricade," police spokeswoman Edna Mamonyane told the Associated Press. "The Metro police found that he was drunk."
The driver was expected to appear in court for a preliminary hearing at a later stage.
Early reports quoted police as saying Nelson Mandela's former wife, Winnie Madikizela, had been in the car when the accident happened.
The foundation told the BBC Ms Madikizela-Mandela was not in the car - which was the only vehicle involved in the crash - but that she had been taken to hospital because of her shock at the news of Zenani's death.
Foundation spokesman Sello Hating said she had been released from hospital after a couple of hours and returned home.
"The family has asked for privacy as they mourn this tragedy," said the foundation in a statement.
In a letter of condolence to Mr Mandela, Fifa President Sepp Blatter described the young girl's death as "unspeakably tragic".
Zenani had celebrated her 13th birthday on 9 June.
South Africa has one of the world's worst road safety records, and there is an average of 42 deaths each day on roads across the country.
Anti-apartheid icon Mr Mandela had campaigned for the World Cup to come to South Africa.
Some 350,000 people are expected to visit South Africa for the competition, which is being held in Africa for the first time.
All the major roads leading to the Soccer City stadium were under severe pressure several hours before the ceremony was due to start, said the BBC's Pumza Fihlani, as fans in thousands of cars tried to make their way into Soweto.
Roads to nearby fanparks - open-air venues where supporters without stadium tickets can watch the matches on large screens - were gridlocked, our correspondent added.
Thursday's World Cup concert had drawn tens of thousands to Soweto's Orlando Stadium, and traffic in the area had been busy into the early hours of Friday.
The event featured a cast of international stars - including Colombian singer Shakira, the Black Eyed Peas and Alicia Keys, as well as African stars Amadou & Mariam and Hugh Masekela.