Gillian Gibbons, 54, from Liverpool, was arrested on suspicion of blasphemy on Sunday.
Ms Gibbons allowed her class of seven-year-olds at the Unity High School in Khartoum to name a teddy bear Mohammed as part of a lesson about animals' habitats.
Mohammed is sacred to Islamic philosophy and the penalty for blasphemy is 40 lashes, a large fine or a jail term. The British Embassy in Khartoum confirmed the arrest.
A source close to the school said one teacher was angered by the naming of the teddy bear and complained to the headmistress.
Ms Gibbons was a deputy headteacher at Liverpool's Dovecot Primary School from 2002 to this July when she left for Sudan.
Her MP, Louise Ellman, told Sky News: "This is very worrying. I understand Ms Gibbons is a very respected person, she is held in the highest regard and is seen as a person of the highest integrity.
"I'm in touch with the Foreign Office and it's right that they should be working hard to bring about a positive end."
There is no specific, or explicit ban in the Koran on images of Allah or the Prophet Mohammed - be they carved, painted or drawn.
However, chapter 42, verse 11 of the Koran does say: "[Allah is] the originator of the heavens and the earth... [there is] nothing like a likeness of Him."
The fear is that images could give rise to idolatry but in this case the response in Sudan, which has been governed by strict Islamic Sharia law since 1983, has been unusually harsh, said Hassan Aberdeen, a researcher at the Oxford Centre for Islamic Studies.
"It seems that the parents made an issue of the teacher calling an animal Mohammed," he said. "Calling him a dog or a pig is insulting, but this is just a teddy bear."
"This could be more to do with who is saying it than what is being said. It might not have been an issue if this was a Sudanese person.
"The fact that this was a European teacher is highly likely to be one of the key causes."