An official in Jigawa state, Usman Dutse, said that the man had confessed to the crime, and had refused an offer to allow him to appeal.
The official did not say when the sentence would be carried out.
He said that the governor of Jigawa, Ibrahim Turaki, would not intervene in the case.
"Nobody has faulted the judgment of the court so he will certainly be stoned to death because that is what Sharia says," he told Reuters news agency.
The Nigerian federal government regards the application of Sharia law in 12 mainly Muslim states in Nigera as unconstitutional, but has so far not acted against its use.
No-one has yet been stoned to death in Nigeria under Sharia law.
But our correspondent says it is difficult to see how the punishment can be avoided.
Other cases
Earlier this week, Nigerian President Olusegun Obasanjo expressed sympathy for a woman, Amina Lowal, whom an Islamic court in the north sentenced to be stoned to death for adultery.
In his first public comments on the case, Mr Obasanjo told journalists he was confident that Amina Lowal's next appeal would be successful - but if it was not, he would weep for her family and for Nigeria.
Ms Lowal conceived a child outside marriage.
A woman convicted under very similar circumstances last year won her appeal a few months ago.
Several thieves have however had their hands amputated.
Supporters of Sharia say they will not be deflected from upholding laws they see as the will of God.
The introduction of Islamic holy law - or Sharia - in northern Nigeria's mostly Muslim states in the past two years has sparked violence in which hundreds of people have been killed.