The match will now be played on Wednesday at 1845GMT.
An downpour at 1530GMT was followed by persistently heavy rain, leading referee Bjorn Kuipers and UEFA officials to carry out an inspection of the pitch 50 minutes before the scheduled 1845GMT kickoff at the Etihad Stadium.
The pitch appeared to drain well when the rain relented soon afterwards but the game was called off about 20 minutes before it was due to start.
"Torrential rainfall across Manchester throughout the evening led to flooding in the areas around the ground, which forced the decision on safety and security grounds," a statement from the club said.
It is the second time in a month Moenchengladbach have had a game called off owing to rain after a friendly against Inter Milan on Aug. 10 suffered the same fate.
City had a friendly with Manchester United in Beijing cancelled in July as a result of heavy rain.
"We are disappointed for the fans because 90 percent of them will probably not be able to watch the re-arranged game," said Moenchengladbach midfielder Oscar Wendt.
"But if the decision had to be taken for safety reasons then we understand it and respect it."
(Editing by Martyn Herman)
