Some fans on social media were scathing, questioning why the world's top drivers could not be let loose in the wet conditions and recalling previous races in the principality held in torrential downpours.
Mercedes's seven-times world champion Lewis Hamilton, who had said after Saturday's qualifying that he hoped rain would mix things up, said he had wanted to go racing.
"We are Formula One drivers, so that is definitely not a good reason," the Briton said when told the delay was because there had been no practice running on wet tyres earlier in the weekend.
"I was, like, let's go when it was just drizzling a little bit at the beginning. We will talk about it in the drivers' briefing but we should have started the race," he said.
A spokesman for the governing FIA said a long second delay had been caused by a power outage, knocking out start systems.
The decision to hold rolling starts, rather than standing ones, was because some drivers would have been disadvantaged by wet asphalt when others were on the dry.
The stoppage after Mick Schumacher crashed was for safety reasons, with the barrier needing to be repaired. The race was ultimately shortened to 64 laps from 77.
Formula One has two race directors sharing duties after previous incumbent Michael Masi was removed following a safety car controversy at the 2021 season-ender in Abu Dhabi that decided the outcome of the championship.
On Sunday, drivers did two formation laps behind the safety car before red flags were waved and the cars returned to the pits.
"It's raining like crazy," Ferrari pole-sitter and local favourite Charles Leclerc said over team radio before the race director called the halt.
The start was originally scheduled for 1500 local (1300GMT) but the formation lap was delayed to 1509, when the rain was not heavy, and then 1516 behind the safety car as conditions deteriorated.
The race finally started at 1605 local, with the field doing a further formation lap behind the safety car.
Red Bull team boss Christian Horner, whose Mexican driver Sergio Perez won the racewith championship leader Max Verstappen third, suggested they could have got going at the appointed time.
He said it was correct to stop it later, however.
Monaco is famous for a lack of overtaking on the tight and twisty streets but slippery conditions make the chances of a mistake far greater.