The baby girl later died, according to the Courier-Mail, and a report is now being prepared for the coroner.
One witness said the parents were in an extreme state of shock.
"I've seen shock before but this was beyond anything I'd ever seen," he told the publication.
He added it was "heroic" the father managed to call emergency services in the circumstances.
Another witness said it was "sickening" to see "a family torn apart in one quick moment".
Council workers capture bird
The magpie believed to be responsible for the fatal attack was captured and removed by council workers this afternoon, according to the Courier-Mail.
Brisbane City Standards chair Kim Marx confirmed an investigation was under way after the incident.
"This is an extremely tragic accident and our hearts go out to the family involved," Marx told the publication.
She added there were several signs in the area warning of magpie swooping, and council officers were in the process of erecting more.