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.
He is believed to have converted in order to marry Rabia Clarke, a Muslim.
This is the fourth marriage of Mr Mandela, 42.
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 chiefs sometimes lead thanksgiving rituals for ancestors, which would include presenting slaughtered animals to them in prayer.
Such practices are not considered to be in line with the beliefs of many Muslims.
Analysis: Pumza Fihlani, BBC News, Johannesburg
Chief Mandla 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 Mr Mandela has 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 Ms Clarke 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: South Africa’s 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.