A ministry statement Friday said the woman, a Spaniard, was arrested on returning from Turkey where she had gone with her family with the intention of joining IS. It gave no further details.
It was the sixth such arrest this week.
On Wednesday, police arrested two people of Moroccan origin in the northeastern town of Cornella de Llobregat on suspicion of recruiting militants for the armed group.
A day earlier, police in Madrid arrested three Moroccans suspected of preparing to carry out an attack in Spain for IS.