The area has been deluged by steady rain over the last two weeks and fresh showers early on Wednesday prompted match officials to abandon play with the toss yet to take place.
The match is the first Test to be played at the Shahid Vijay Singh Pathik Sport Complex, which has only basic drainage systems, though it has hosted 11 'home' limited-overs matches for the Afghans.
Afghanistan play their home matches abroad due to security concerns for touring teams.
In response to criticism about the choice of venue, an Afghanistan Cricket Board official told local media they chose Greater Noida ahead of two other options in India because of its proximity to Delhi, which made travelling from Kabul easier.
"If it rains like this, no venue is going to be able to host a game," Menhajuddin Raz, ACB's international cricket manager, told reporters on Tuesday.
The ACB said in a statement they had ruled out playing in the United Arab Emirates due to the extreme heat there.
"It's important to understand that the Future Tours Program (FTP) is typically planned five years in advance, which makes it nearly impossible to predict future circumstances with complete certainty," the board said.
With more rain forecast for the rest of the week the match could become just the eighth Test to be abandoned without a ball being bowled.
Match referee Javagal Srinath's report to the International Cricket Council (ICC) will determine if the venue would incur any sanctions from the governing body.
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