Repeated heavy rain showers and the approach of darkness meant only Q1 could be run on Saturday.
Q2 and Q3 will now take place at 11am local time, six hours before the scheduled race start.
Red Bull team boss Christian Horner said the organisers made the right call.
"It is a shame because of the weather but absolutely the right decision was made to stop the qualifying and postpone it for tomorrow," he said.
"The conditions were just deteriorating too quickly with the daylight and too much standing water.
"Hopefully it will blow through and we will be back in the morning."
McLaren sporting director Sam Michael said the main issue was how hard the repeated showers were, leaving only fleeting periods of acceptable track conditions.
"It was too wet and the visibility is pretty poor," he said.
"When they started Q1 it was right on the limit of aquaplaning on the full wet.
"Fortunately then it did get to a point where you could get onto inters, which Jenson Button judged very well and then everyone followed.
"From that point it went 'bang', full wets again. It was a narrow window and that was it."
Ferrari's Felipe Massa was one of several drivers who crashed during Q1. He was able to return to the pits with front end damage after spinning into the wall on the exit of Turn 2.
"I lost the car because I just touched the white line without trying to do anything," he said.
"I was very lucky to carry on given the way I hit, the way I crashed."
He confirmed that the slippery circuit marking lines were a bigger issue than standing water.
"It's more white lines than aquaplaning, but when it's raining a lot they need to stop."
McLaren driver Jenson Button hoped F1 did not receive too much criticism for the rain delay.
"There are so many sports that don't play if it is raining, motorsports and other sports," he said.
"We have a car and tyres that are good enough in certain conditions but this is impossible, and it is not just about the show when it is like this.
"This is way too dangerous - and it is sad. Hopefully the fans understand that and we will make sure we do a great job in the morning."