The tie will now take place on January 19, which was originally the date for the second leg. That match will now take place on Wednesday, January 27.
Tuesday night's other semi-final clash between Rovers and Villa haalso fallen victim to the weather.
The decision means the Premier League games between United and Hull and City and Stoke, due to be played at Old Trafford and the Britannia Stadium on Tuesday, January 26 and Wednesday, January 27 have now also been postponed.
In an ideal world, the clubs would have preferred the game to go ahead as planned on Wednesday. But they accepted there was no hope of that happening once Manchester had been hit by such a hefty snowfall.
City and United, who train close to each other at Carrington, were forced to cancel their sessions on Tuesday and tell their players not to report for duty.
Indeed, advice for the general public has been to stay indoors unless absolutely necessary, with City closing their Eastlands ticket office due to the atrocious conditions.
As with Blackburn, the problem at Eastlands is not anything to do with the pitch. The surrounding roads are in a terrible mess and local motorways are also at a standstill in certain areas.
Under normal circumstances, the games would have been rearranged for next week on the same days.
However, with City's Premier League encounter with Blackburn due to be broadcast on ESPN on Monday evening, that was ruled out.
Stoke are also monitoring conditions ahead of their Premier League fixture against Fulham on Tuesday night but have so far said they are "confident'' the game at the Britannia Stadium will go ahead.
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