Queensland MP Gavin King said the local community does not want the house to remain at its Murray Street site in the suburb of Manoora.
"It is the right thing to do to help with the healing process," he said.
A memorial for the eight children would be established after consultation with the family and local community.
King, however, said it had not yet been decided what type of memorial would be built but the government would be guided by community wishes.
37-year-old Mersane Warria has been charged with the murder of her seven children and her niece.
She's been refused bail and is recovering from stab wounds in Cairns Hospital.
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