The West End Redbacks required eight wickets and the Vics 102 runs for victory, but Tuesday's final day was abandoned without a ball being bowled.
A heavy shower swept Melbourne and soaked the MCG outfield. Conditions improved somewhat in the afternoon, however intermittent rain continued to cause delays.
The match was abandoned at approximately 5pm local time.
Victoria’s Scott Boland was named Player of the Match for his seven-wicket haul in the opening innings.
Redbacks bowler Chadd Sayers provided one of the highlights for the visitors by crunching his maiden first-class half-century late on Day 3 in what proved to be a pivotal innings for South Australia.
Veteran batsman Tom Cooper also crushed his second consecutive ton following an outstanding 178 against Queensland.
The Redbacks sit in fourth place on the Shield table with three draws from three matches while Victoria retain top spot recording two wins and a draw.
South Australia host Western Australia at Adelaide Oval from Friday, November 16 in Round Four of the Sheffield Shield.