In its statement, the South African National Editors Forum said it found the threats against Mamabolo deeply disturbing.
"Such threats have no place in a democratic society and underline the risks that journalists face when covering the activities of politicians at all levels including branches, regions, and provinces. We hope that SAPS will take this threat against the journalist seriously and carry out the necessary investigation.
"We hope that the MP responsible for the threats will be brought to justice to show that this unparliamentary behaviour has no place in our democracy. We also call on the ANC to show that it does not tolerate such behaviour within its ranks and that it will duly take steps to discipline its member."
In March, EFF leader Julius Malema and his wife, Mantoa, approached the Limpopo High Court on an urgent basis, seeking R2 million in damages from Mamabolo.
This came after Mamabolo accused Malema of abusing his wife during the State of the Nation Address in Parliament. Mamabolo was served with papers demanding R2 million for defamation.
The two parties eventually reached a settlement before the merits of the case was argued in court.