Other suspects have faced prosecution in Germany, but they either came back on their own or were deported from another country. Germany has, however, taken children out of camps in Syria.
The group arrived at Frankfurt Airport late Saturday on a flight from Erbil, Iraq. They had previously been in northern Syria, federal police said.
Law enforcement authorities in the western German state of Hesse will now take over her case, the federal police said.
The 30-year-old is being investigated on suspicion of membership in a terrorist organization and child neglect, said a spokesman for the attorney general's office in Frankfurt.
However, a warrant has not yet been issued for her arrest.
In addition to her own children, she also had a 2-year-old girl with US citizenship in her care. The US child's connection to the suspect was not immediately clear.
The family had last lived in the al-Hol prisoner camp in northern Syria, sources told dpa. Al-Hol is sprawling camp that houses tens of thousands of people, including Islamic State detainees and their families.
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