The man and woman were buried up to their necks, then pelted with stones until they died.
Aguelhok in the region of Kidal was one of the first to be captured by Tuareg separatist rebels.
The Islamists in Aguelhok stoned the couple to death in front of about 200 people, officials said.
"I was there. The Islamists took the unmarried couple to the centre of Aguelhok. The couple was placed in two holes and the Islamists stoned them to death," a local government official told the AFP news agency.
"The woman fainted after the first few blows," he said, adding that the man had shouted out once and then fallen silent.
A Tuareg rebellion in northern Mali triggered a military coup in March and in the ensuing chaos Islamist groups seized control of several towns in the north.