The teacher, who the British Foreign Office identified as Gillian Gibbons, was arrested Sunday after she named the bear Muhammed and wrote the name on the toy animal, the official center said in a statement.
The British Foreign Office said Gibbons, 54, was arrested after she had allowed her 7-year-old pupils to choose a name for a stuffed teddy bear, and they chose the name Muhammad.
The Sudan Media Center, quoting attorney Mutasim Abdalla Mohamed of the Khartoum North attorney's office, said legal procedures were under way against Gibbons, who taught at the Unity High School in Khartoum, after a complaint was filed by the Ministry of Education.
The ministry was acting on the behalf of a parent of one of Gibbons' students, the center's statement said.
An attempt to reach the school by telephone after school hours Monday went unanswered.
A Sudanese government official, who spoke on condition of anonymity because he was not authorized to speak to the media, confirmed that Gibbons was still being detained Monday pending the completion of the investigation.
Abdul Mageed Khogalli, a member of the government's Commission for Non-Muslims, said he was aware of the case but could not comment.
The British Embassy in Khartoum did not return calls for comment.