The result, with Hamilton finishing third after leading most of the way, slashed the double Formula One world champion's overall lead to 10 points after six of the season's 19 races.
The Briton had started on pole position and did not put a wheel wrong until he pitted for fresh tyres when the safety car was deployed with 14 laps to go.
"I've lost the race haven't I?" the disconsolate driver enquired over the team radio after rejoining in third place behind Rosberg and Ferrari's Sebastian Vettel, neither of whom pitted. "What's happened guys?"
Afterwards, with the enormity of what had happened still sinking in, the stunned Mercedes driver told reporters: "I can't really explain the way I feel at the moment. I won't even attempt to."
While he did not blame the team, Mercedes motorsport head Toto Wolff indicated the call had come from the pitwall: "We thought the gap was different to what it was. A complete misjudgement, I am so sorry," he told the BBC.
"We screwed it up for him."
The safety car had been deployed after Dutch 17-year-old Max Verstappen's Toro Rosso smashed into the back of Romain Grosjean's Lotus and crashed heavily into the barriers while fighting for a possible 10th place.
GRID PENALTY
Verstappen, who had provided some of the more exciting moments of a largely processional race, was unhurt although the front of his car penetrated the plastic wall at the Sainte Devote corner.
Stewards later handed him a five-place grid penalty for the next race in Canada.
Rosberg's victory was the German's second in succession, after winning the previous round in Spain, and made him only the fourth driver to win three Monaco Grands Prix in a row. The others were Graham Hill, Ayrton Senna and Alain Prost.
"I'm very, very happy of course. I know it was just a lot of luck today. Lewis drove brilliantly and would have deserved the win for sure but that's the way it is in racing," said the Monaco resident.
"I’m aware I got lucky, very lucky, probably the luckiest I’ve ever been in my career, but I’ll take it and enjoy it," said the German. [L3N0YF0BJ]
Russian Daniil Kvyat was fourth for Red Bull with Australian
team mate Daniel Ricciardo fifth, after swapping places at the end, and Kimi Raikkonen finished sixth for Ferrari.
Mexican Sergio Perez was seventh for Force India while Britain's Jenson Button handed misfiring former champions McLaren their first points of the season with eighth place.
"To come in now, sixth race with a brand new engine and everyone else has had a season with the new engine in, and to score points feels like winning a race," said Button.
Brazilian Felipe Nasr was ninth for Sauber with Verstappen's Spanish team mate Carlos Sainz taking the final point for Toro Rosso after starting in the pit lane.
In a novel touch decided by local organisers, the familiar 'grid girls' who stand in front of cars on the grid were replaced by male models.
(Reporting by Alan Baldwin, editing by Justin Palmer)
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