The FPÖ’s original choice of 21-year-old Krauss for vice president of the school board, which provides educational and psychological support for parents and students, was widely criticised in the Austrian capital.
The FPÖ is the second largest party in the city council, and so it falls to them to make the appointment.
Krauss was known for calling Mayor Häupl the "mayor of the Turks (who) takes his orders directly from Ankara".
He had also demanded that "immigrants with Turkish blood (be) sent back where they came from" and called for foreign children to be put in separate classrooms because their German is not good enough.
Häupl’s office said that the current vice president, Helmut Günther, must stay in office until the FPÖ has nominated a suitable candidate.
Human rights organisation SOS Mitmensch welcomed the decision. "A person who stirs up hatred and divides children and young people according to their origin and religion, has no place in the city council," said spokesman Alexander Pollak. "His appointment would have been a slap in the face of many students."