Tutu, who is retired as the Anglican archbishop of Cape Town, and Mandela worked closely together during the struggle against apartheid, and Tutu headed the Truth and Reconciliation Commission after Mandela became president. Both men were awarded the Nobel Peace Prize for their work.
Tutu said he had made arrangements to fly to the Eastern Cape for the funeral and burial but has now canceled them, the (South Africa) Independent reported.
"Much as I would have loved to attend the service to say a final farewell to someone I loved and treasured, it would have been disrespectful to Tata to gatecrash what was billed as a private family funeral," he said.
"Had I or my office been informed that I would be welcome there is no way on Earth that I would have missed it."
Mac Maharaj, a spokesman for President Jacob Zuma, said Tutu has been invited and described him as "an important person." Tutu has been critical of Zuma, saying before the 2009 election he was not sure he would bother to vote.