The 54-year-old from Liverpool was officially detained Sunday for allegedly insulting Islam's prophet, Britain's Sky news reported.
Her 6- and 7-year-olds chose the name as part of a school project back in September.
A spokesman for the British Embassy in Khartoum said Gibbons taught at Unity High School in central Khartoum, which was closed Monday for fear of reprisals, Time magazine reported.
"We are in contact with the authorities here and they have visited the teacher and she is in a good condition," the spokesman said.
Another source close to the school said the incident was blown out of proportion after one teacher at the school was angered by the naming and complained to the headmistress.
Gibbons is accused of insulting the Prophet Mohammed, violating article 125 of the Sudanese criminal law, which covers insults against faith and religion.
Time said Gibbons faces a possible public lashing or up to six months in prison if convicted of blasphemy.
Notable deaths of 2014 [PHOTOS]