The demonstrators made their way to Khartoum's presidential palace for a rally while others burned newspapers that contained pictures of the teacher.
But they steered clear of Unity High School, where Gibbons worked. The school was guarded by police in riot gear.
Under Sudan's penal code, Gibbons could have been sentenced to 40 lashes, a fine or up to a year in jail.
Teachers at the school say that naming the teddy bear Mohammad was not Gibbons's idea.
They say no parents objected when she sent them circulars about a reading project that included the bear, introduced to the class in September, as a fictional participant.
David Miliband, Britain's foreign minister, said he was "extremely disappointed" with the verdict and called in the Sudanese ambassador for an immediate explanation.