Prime Minister Julia Gillard said in a statement that she was deeply saddened by the passing of one of the nation's pioneering female political leaders on Saturday night.
Ms Child became the first female Labor member of the House of Representatives when she won the east Melbourne seat of Henty in 1974.
She was only the fourth woman to be elected to the House.
Her family have taken up the offer of a state funeral.
Ms Gillard said Ms Child was widowed at a young age, and raised five boys on her own and for a time worked as a cleaner to make ends meet.
"She came to politics later in life, bringing remarkable gifts of common sense, good humour and persistence against the odds," Ms Gillard said in her statement.
"Though she attained high office, Joan always retained a sense of perspective; her hobbies - gardening, reading detective fiction, listening to her idol Elvis - kept her firmly grounded.
"As a confirmed true believer, Joan never forgot who had put her into politics or why. She was a powerful voice for the needs and rights of women, especially working women and women doing it tough.
"Joan Child displayed great purpose and dignity in public life, setting an example that led the way for women's participation in the modern Labor Party.
"Joan Child will remain for me an abiding source of inspiration."