The first phase of the session at Ferrari's home circuit was red-flagged after four minutes when Grosjean's Haas went into the barriers, triggering an angry outburst from the driver.
"We should have not gone out at all. I am pretty straightforward about that," he said.
"The impact wasn't strong -- I hit the barriers at an angle but spinning on a straight shouldn't happen in Formula One".
The session was pushed back 15 minutes at a time, with the safety car deployed to test the conditions, but the rain continued to fall as fans became increasingly frustrated by the lack of action.
Final practice in the morning was also mostly washed out.
Two hours after the afternoon qualifying session had started, and an hour after it had been due to end, only nine drivers had completed timed laps in the few minutes of track action before the stoppage.
Last year's race, won by now-retired world champion Nico Rosberg for Mercedes, lasted only an hour and 17 minutes in comparison.
Monza is the fastest track on the calendar, with long straights and cars reaching well in excess of 300kph, and the risk of aquaplaning off in such conditions is high.
"I don't know what is happening with the cars and tyres but we cannot take risks with the drivers. But it's hard to accept for the fans," four-times world champion Alain Prost told BBC radio as drivers waited.
Formula One has held qualifying on the morning of the race before, most recently the rain-hit U.S. Grand Prix in Austin, Texas, in 2015.
"This is a difficult afternoon for all the drivers and all the teams. I would rather wait until tomorrow and have a dry qualifying and dry race," commented the Mercedes team's non-executive chairman Niki Lauda.
A fourth successive pole position at Monza for Mercedes' Lewis Hamilton would be the 69th of the Briton's Formula One career, beating the record he currently shares with seven-times champion Michael Schumacher.
Hamilton is seven points behind Ferrari's Sebastian Vettel and will take the overall lead if he wins the last European race of the season.
While waiting, the triple world champion spent his time engaging with fans on social media.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
