Garg, 21, was a graduate accounting student at an Australian university.
His killing is the latest in a series of attacks on Indian students in the country.
Police said the motive for the attack, which they described as "vicious", was not known.
Media in India have labelled the series of attacks against Indian students in Australia as racist, but police and the Australian government have said the attacks are criminal, not racist.
SM Krishna, the Indian external affairs minister issued a statement on Sunday, condemning the "brutal attack", with Indian media warning the attacks were creating "deep anger" in India and could have a "bearing on bilateral ties".
|While many in India see the the attacks as racist, Australia says they are criminal [AFP]
"There is extreme shock and fear and anger," Gautam Gupta, a spokesperson of the Federation of Indian Students of Australia, told local radio on Monday.
Australia's international student sector is the country's third largest export earner, behind coal and iron ore, totalling $11.7bn in 2008.
Attacks against Indian students in 2009, mainly in Melbourne, led to protests by students and strained bilateral ties, prompting Gillard and other Australian ministers to visit India to offer assurances that everything was being done to stop the attacks.
Australian universities also sought to reassure students and their families that Australia was a safe place to study.
But a recent study forecast a 20 per cent drop in Indian students in 2010 due to the attacks.