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Football's governing body issued a statement on Wednesday night calling for calm among fans.
"FFA has become aware that Sunday Telegraph journalist Rebecca Wilson has received physical threats and death threats," the FFA's statement said.
"While these are matters for the Police, FFA has called for these threats to cease."
Wilson has come under fire after she was the author of a Sunday Telegraph article that displayed the photos, name and ban details of 198 barred A-League fans.
The threats have taken their their toll on Wilson, who admitted the messages had made her deeply upset.
"I have had death threats today and have had some seriously bad stuff sent to me today," Wilson said on Sky News' Sports Night.
"It’s pretty unusual but I cried today."