The prince has spoken to City Press after rumours in high social circles that their marriage is on the rocks.
Princess Zenani is often seen in the company of her famous father at state functions, including when Mandela was inaugurated as state president in 1994. He is reportedly deeply saddened by the troubles in the marriage of his daughter.
The prince has confirmed Mandela has asked them not to part during family meetings convened to bring about reconciliation between the two.
Prince Dlamini, who admitted he was no longer living with Zenani, said he loved his wife very much.
It is understood the couple has been living apart for about two years, fuelling rumours of an impending divorce in this family that is regarded by many as part of South Africa's own "royalty".
"Every family has its problems. I love Zenani.
"She will not go anywhere because she was married in the traditional Swazi way," said Prince Dlamini.
"In my culture if a woman is married in the traditional way, she remains your wife despite any problems arising from the marriage.
"Zenani is my wife and she was blessed by my father during our wedding in Swaziland," the prince said.
The couple were married in 1977 and their traditional wedding was witnessed by the prince's late father, King Sobhuza II.
On and off
A close family friend said the couple's marriage has been on and off.
The friend pointed out they have not been seen together at public functions for some time and there was "a dark cloud over the marriage".
Last week, the couple's son Ntsiki graduated at Rand Afrikaans University. Only the father was seen with grandmother Nomzamo Madikizela in attendance.
It is understood efforts to save the couple's marriage have not succeeded so far.
Princess Zenani declined to talk when contacted for comment. She gave her cellphone to her children who responded by saying their mother was not available to talk to us.
A young woman who responded when we tried to contact Zenani said problems within the family were "nobody's business". She said she was Zenani's daughter.