Stephanie Banister, 27, was contesting a seat in Queensland for the anti-immigration One Nation Party. She had only been in politics for 48 hours.
Banister also confused the term "haram" (forbidden) with the holy Koran and suggested Jews worshipped Jesus Christ.
The interview, which aired early this week, went viral on social media.
''I don't oppose Islam as a country, umm, but I do feel that their laws should not be welcome here in Australia,'' Banister told Seven News reporter Erin Edwards.
She announced her withdrawal from the election on Saturday.
"With the way Channel Seven edited my interview, I was left quite the fool," Banister said in a brief statement.
"I'd like to apologize to One Nation, to my friends and family, for any embarrassment this has brought to them."
One newspaper headline said Banister had managed to put Islam literally on the map.
The leader of One Nation, Jim Savage, said Banister continued to have the "full support" of the party executive.
He said she had been under "enormous pressure", including threats to her and her family.
Commentators compared Banister to Sarah Palin, the gaffe-prone Republican vice-presidential candidate in the 2008 US election.
Even before this interview, Banister was regarded as a rank outsider to win her seat in Sydney.
The mother-of-two rose to prominence when she was arrested for going into a supermarket and putting stickers saying "halal food funds terrorism" on Nestle products.
She is facing charges of "contaminating or interfering with goods". If convicted before polling day, she would have been barred from standing.
NTJ/SHI