The woman was released from custody late on Saturday night.
"She was released at 11.30pm. She is free and can go wherever she wants," said Lower Saxony's prosecutor Thomas Klinge to Swedish news agency TT.
Prosecutor Frieda Gummesson submitted a new warrant for her arrest on Thursday. She then issued a European arrest warrant (EAW). At the remand hearing held on Saturday the woman status as a suspect remained unchanged and was therefore of an insufficiently high grade for an EAW.
A European arrest warrant (EAW) replaces extradition arrangements among EU member states. An EAW can only be issued if the grade of suspicion is of the highest order.
Gummesson pointed out that the 31-year-old remains a suspect.
It is now the job of the police investigating the murders to produce sufficient information in order to allow for the issuing of an EAW.
"At the moment I am unable to say how long this will take," said Gummesson, adding that "the German authorities are obliged to work according to their guidelines."
On Thursday German authorities began an investigation against the woman, before an EAW had been issued.
The children and their mother were found with serious stab wounds at their home in Arboga, central Sweden on Monday evening. The children later died from their injuries.
Police have not yet been able to speak to the mother, who was seriously injured and remains under observation at Uppsala University Hospital.
TT/Peter Vinthagen Simpson