Faruqi took office a week after Senator Fraser Anning, of Australia's Katter Party, made controversial comments on Muslim and non-English speaking immigrants from the "third world", reports Efe news.
"After last week particularly, it is really good to have you here," Labor Party leader Penny Wong said in the Senate, referring to remarks by Anning, who also called for a plebiscite on immigration.
Farqui migrated to Australia from Pakistan in 1992 and represented the Green Party in the New South Wales Legislative Council since 2013.
She replaces Lee Rhiannon from the Green Party, WHO announced her retirement in May.
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