The region is predominantly Muslim.
Muslim students at the Shehu Shagari College of Education reportedly killed the woman and set her body alight.
They then went on the rampage destroying property including vehicles.
A police spokesperson in Sokoto state told the BBC that security forces intervened to restore calm and an investigation was under way.
The authorities have shut down the college indefinitely and ordered students to go home immediately.
Nigeria’s most senior Islamic religious leader, the Sultan of Sokoto, Sa’ad Abubakar, has condemned the killing of the Christian student and appealed for calm.