With rain deluging Boca's famous La Bombonera stadium, officials took the decision to reschedule kick-off for Sunday at 4pm local time (1900 GMT).
"For reasons of force majeure the game is suspended for tomorrow at 4pm," South American football's governing body CONMEBOL announced on Twitter.
The announcement came roughly 95 minutes before Saturday's first leg was scheduled to kick off, with fans already in their seats at the Bombonera.
The game had been in doubt for several hours with Buenos Aires drenched with unrelenting rainstorms.
Huge puddles of water could be seen on the Bombonera pitch while water several inches deep flowed in parts of the stadium.
The postponements means the football world will have to wait for what promises to be an epic battle between Boca and River, fierce local rivals who are meeting in the final of South American football's top club competition for the first time.
The match -- known as the 'Superclasico' -- had been billed as the "Game of the Century", with tickets reportedly changing hands for up to $25,000 on the black market for the once-in-a-lifetime clash.
The return leg, at River's Monumental stadium on November 24, will be played before a full house of 67,000.