The first-ever test scheduled between the sides looked doomed from the start due to steady rain for more than two weeks in the region. It was also the first test to be scheduled at the Shahid Vijay Singh Pathik Sport Complex near Delhi.
Afghanistan play their home matches abroad due to security concerns for touring teams.
The Afghan board preferred Greater Noida over two other venues in India because of its proximity to Delhi, which made travelling from Kabul easier.
"We're disappointed. We'd geared ourselves up, and we'd trained really well," Afghanistan coach Jonathan Trott told reporters.
"What I hope it is a good learning case that things can crop up... everything has got to be checked out and made sure that it's ready for test match cricket.
"I think the ground staff have worked, obviously, very hard here. It just unfortunately hasn't materialised, and we've had a freakish amount of rain for this time of year."
New Zealand coach Gary Stead was frustrated after they were denied an opportunity to get used to the sub-continent's conditions ahead of a busy schedule that includes five more tests in Asia in the next two months.
"The most disappointing part for us is that we lost the opportunity to be match-hardened and match-ready when we go into our test match (against Sri Lanka) next week," Stead said.
"The guys are really disappointed. It was an opportunity to play Afghanistan. It doesn't come around that often."
New Zealand will fly to Sri Lanka on Saturday for a two-test series in Galle from September 18th.
