The victim was beaten to coma before she was set ablaze.
The incident had triggered outrage on social media as many Nigerians condemned the act.
In a statement issued in Sokoto, Kukah said Muslims and Christians had lived together peacefully for a long time.
He described those behind the barbaric act as criminals.
“We condemn this incident in the strongest terms and call on the authorities to investigate this tragedy and ensure that all the culprits are brought to book. The only obligation that is owed her immediate family, her fellow students and the school authorities is the assurance that those who are guilty of this inhuman act, no matter their motivation, are punished according to the extant laws of our land.
“This has nothing to do with Religion. Christians have lived peacefully with their Muslim neighbours here in Sokoto over the years. This matter must be treated as a criminal act and the law must take its cause,” he said
He however, called on all Christians in Sokoto and around to remain calm and to please pray for the repose of the soul of Ms. Deborah. It is the first obligation we owe her.”
Meanwhile, Sokoto State Police Command has announced the arrest of two suspects over the killing.