The appointment of Gene Robinson as the first homosexual bishop by the Episcopalians in the United States has threatened to split the Anglican Church and its 70 million followers worldwide.
The crisis has prompted the Archbishop of Canterbury, who heads the Anglican community, to call an emergency summit.
"For us that doesn't make a difference, the sexual orientation," Tutu told Reuters Television on Sunday in South Africa's sprawling Soweto township.
"In our Church here in South Africa, the Anglican Church in South Africa, that doesn't make a difference. We just say that at the moment we believe that they should remain celibate and we don't see what all the fuss is about," he added.
Tutu was attending a farewell ceremony for Bishop Mvume Dandala who is to head up the All Africa Conference of Churches in Kenya.
Kenya's Archbishop Benjamin Nzimbi said on Sunday its Anglicans may sever ties with the Episcopalians, the US branch of the Church.
"I am saddened that this issue is causing so much division in the life of the Church."
Bishop Mvume Dandala
"We are thinking of cutting ties," Nzimbi told Reuters in Nairobi. "Homosexuality is not accepted. This practice is against the word of God."
Dandala has until now served as the presiding bishop of South Africa's Methodists who have developed increasingly close links with the Anglicans. He said he was saddened by the furore.
"I am saddened that this issue is causing so much division in the life of the Church. My hope and prayer is that the Church is going to continue discussing this matter, that whatever decision people come to, that it will be handled in a powerful pastoral way," Dandala said.
On Friday Archbishop of Canterbury Rowan Williams summoned Church leaders to an emergency summit in October to discuss the appointment of Gene Robinson, an openly homosexual priest, as bishop of New Hampshire by the Episcopalians.
Last month Williams averted a similar split over plans to appoint another homosexual priest as a bishop in England. The priest declined the post after an outcry from conservatives.
Anglican churches are independent in each country but liase closely on spiritual matters.