A police official told the AFP news agency that the Sanaa blast "is a purely criminal incident," suggesting that the attack was not linked to the US embassy.
But Tom Casey, US state department spokesman, said he thought it was "fairly safe to assume that the embassy was at least a potential target if not the target".
He said that unknown individuals had fired three mortar rounds in the vicinity of the US embassy.
"While obviously there needs to be an investigation I think the general sense was these things were fired in the general direction of the embassy," Casey said.
A Yemeni interior ministry official told the Associated Press news agency that the attack was likely linked to a dispute between a teacher and the school's administration.
He said the school had received a warning two days ago from the teacher's family about an imminent attack.
Troops were deployed to the area, sealing off roads and preventing journalists from reaching to the site of the blast. In 2007,
Yemen banned people from bringing weapons into its major cities in an attempt to stem crime and violence in a country with one of the highest rates of gun ownership in the world.