Menzel was originally slated to play the historic New York venue on Monday (October 29), but delayed the gig due to the 'Superstorm' making landfall in the city.
Her Carnegie Hall show was then rescheduled for November 4, but has now been delayed again to January due to attempts by New York authorities to secure a dangling crane attached to a local skyscraper.
Menzel explained the delay in a message to fans on Twitter: "First it was Frankenstorm, now it's Frankencrane. Sorry about another cancellation. Hope you can all join me in January! Most importantly, be safe and look out for each other."
Hurricane Sandy has caused tremendous damage throughout the East Coast of the US in recent days.
More than 90 people have died and thousands of others have lost property due to mass flooding, particularly in New York and New Jersey.
NBC is hosting the telethon Hurricane Sandy: Coming Together for the victims tonight (November 2) at 8/7c, while ABC will organise a 'Day of Giving' across its network programming on Monday (November 5).