Painter and decorator Gary Hawken was buried in St Dennis cemetery in Cornwall in September.
But a woman pointed out she had already bought the plot in 2006 following the burial of her mother in the cemetery.
The parish council, which owns the cemetery, said there had been a "humongous mistake" which is now being dealt with by lawyers.
Mr Hawken's brother, Paul, told the Western Morning News the situation was "heart-breaking".
He said: "We've said prayers at his graveside and then they say we have to have him exhumed and moved from that resting place.
"It's like they are talking about a cat or dog we've buried at the bottom of the garden, but it isn't."
Julia Clark, chairman of St Dennis Parish Council, said: "Something went horrendously wrong."
The woman who bought the plot, whose name is not known, has told the parish council she wishes to retain ownership.
Mrs Clark met the Hawken family and told them Mr Hawken may have to be exhumed if the owner will not accept a different plot.
Mrs Clark said the council would do all it could to avoid a situation where Mr Hawken had to be exhumed.
She said: "A humongous mistake has been made. We are trying to unravel what happened."
A man buried in the wrong cemetery grave may have to be dug up and reinterred.