The Congress of Traditional Leaders in South Africa (Contralesa) told the BBC that being Muslim could affect his ability to uphold Xhosa traditions.
Mandla Mandela, who converted to Islam late last year, got married in a Cape Town mosque last week.
He inherited his position as chief of Mvezo in the AbaThembu clan from his grandfather, Nelson Mandela.
Contralesa’s spokesperson Chief Mwelo Nonkonyane said Mr Mandela’s new religious affiliation could present a conflict for his subjects.
“There is nothing wrong with a traditional leader following any faith he chooses but we are concerned about whether he will be able to continue performing his responsibilities as a chief,” he said.
Traditional leaders are at times called upon to lead thanksgiving rituals for ancestors, which would include presenting slaughtered animals to them in prayer, says the BBC’s Pumza Fihlani in Johannesburg.
Such ritual offerings, which are a key part of traditional ceremonies, are not considered to be in line with the beliefs of many Muslims, our correspondent says.
Analysis: Pumza Fihlani, BBC News, Johannesburg
Chief Mandela Mandela may find himself at a crossroads – forced to choose between his new bride and his loyal subjects.
Nelson Mandela’s heir, who prides himself on being a man of tradition, may face some tough questions over his decision to convert to Islam.
The conversion has implications for him not because of the religion itself but because it creates uncertainty about the chief’s loyalties.
And it seems the secrecy has caused concerns within the AbaThembu Royal family, who now question the chief’s commitment to upholding time-honoured traditions.
In rural South Africa, away from many of the trappings of modern life, traditional leaders play a key role in their communities.
This could be in the form of ceremonies or day to day decisions on how to resolve conflicts. While this is the chief’s fourth marriage, it is the first to pit him against tradition – the very core of who he is.
Mr Nonkonyane says the 42-year-old had already gone against traditional by assuming his wife’s culture.
“According to African tradition, it is the woman that must become part of the family she is marrying into. When she accepted Mandla’s proposal, the expectation was for her to adopt the ways of his people,” he said.
He married Rabia Clarke, his fourth marriage, in a ceremony that was not attended by members of the royal family, leading to reports they were not happy with the union.
Mandla Mandela’s wives:
Married Tando Mabunu-Mandela in 2004. They are reportedly still entangled in a bitter divorce
Wed Anais Grimaud, from Reunion, in a traditional ceremony in 2010. Marriage annulled after reports that she had an affair with his younger brother
Married Mbali Makhathini in 2014. Marriage annulled by court after first wife opened charges of bigamy
Wed Rabia Clarke in a Cape Town mosque in 2016 after converting to Islam
Source :The Times Newspaper
But Mr Mandela seems content with his decision.
“Although Rabia and I were raised in different cultural and religious traditions, our coming together reflects what we have in common: We are South Africans,” he is quoted as saying at the ceremony.
Mr Mandela is also an MP with the governing African National Congress.