Spain's National Court, which is charged with terrorism cases, ordered that the woman be held in jail for the suspected crime of cooperation with a terrorist organisation.
Police arrested the woman along with her husband and two sons yesterday in the northeastern city of Badalona near Barcelona.
The teenagers had been in contact with jihadist recruitment networks and were believed to be on the verge of leaving for Syria via Turkey, the interior ministry said.
The court also accused the woman's husband of "cooperating with a terrorist organisation" but released him on condition that he turn in his passport and present himself to a police station every week while the investigation is carried out.
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The two teenage boys will be questioned by a juvenile court judge.
The interior ministry said the brothers had been under surveillance since a third brother had travelled to Syria, where he is believed to have "joined jihadists groups linked to Daesh (an acronym for the Islamic State group)."