The freeway is named in honour of General Sir John Monash, an esteemed Australian military commander for the allies during World War I.

Construction of the initial section of the South Eastern Freeway by the Melbourne and Metropolitan Board of Works had been completed and opened in 1962,[10] connecting Burnley at Burnley Street, through Cremorne via Harcourt Parade, over Punt Road using a new overpass (known as the Morshead Overpass during construction[11]) to end at Anderson Street and the Morell Bridge, with an at-grade intersection with Brunton Avenue and a single-carriageway feeder road to the Swan Street bridge (and Batman Avenue) 800 metres beyond.

[13] Plans to link the two freeways dated from August 1978, while still extending the Mulgrave Freeway, from a Steering Committee appointed by the government in 1976 to carry out the "Gardiners Creek Valley Study": the study involved the Ministries for Planning, of Transport and for Conservation, the Melbourne and Metropolitan Board of Works, Town and Country Planning Board, Malvern, Camberwell and Hawthorn City Councils and the Country Roads Board, with an extensive process of public consultation.

[14] The subsequent route agreed to was referred to as the "South Eastern Freeway, Malvern Section" and was ultimately the alignment constructed.

[14] Construction of the link as a dual-carriageway road began in 1985,[15] opening to traffic in late 1988,[16] originally with two lanes in each direction, and declared a State Highway.

The project attracted a great deal of controversy just before it opened and well afterwards: in order to save costs, only one freeway-style interchange had been constructed (underneath High Street in Glen Iris).

This led to heavy congestion, frequently kilometres long, on the freeway, fuelling anger and frustration, and attracting a moniker of "the South-Eastern Carpark".

In the late 1990s, construction of CityLink's Southern Link project began, with the aim of linking the north-western end of the freeway (then terminating at Batman Avenue) to the eastern-end of the West Gate Freeway by way of tunnels underneath the city, allowing for an uninterrupted voyage past the CBD.

[19] Before this bypass was constructed, the sweeping curve of the freeway at the Hallam end that became the South Gippsland Freeway had its capacity reduced from three lanes to two, resulting in a notorious bottle-neck at peak hours, especially for outbound traffic exiting at the Princes Highway interchange outside Dandenong; the extension finally bypassed the entire problem.

Construction on the 7.5 km-long (4.7 mi) Hallam Bypass, linking the Monash Freeway to the Princes Freeway in Berwick, began in the 1999/2000 financial year,[22] and was completed after 3 years of construction to open in July 2003, 17 months ahead of schedule and $10 million under budget for a total cost $165 million.

[23] This was due to the omission of one key interchange that should have linked the South Gippsland Freeway with the Hallam Bypass at Eummemmering[citation needed].

The passing of the Road Management Act 2004[24] granted the responsibility of overall management and development of Victoria's major arterial roads to VicRoads: in 2004, VicRoads re-declared Monash Freeway (Freeway #1000) from the "Southern Link Tollway" (CityLink's Southern Link) at Kooyong to Princes Highway in Narre Warren.

This section runs through south-eastern metropolitan Melbourne, including the suburbs of Chadstone, Mount Waverley, Mulgrave, and Dandenong to Doveton.