Rosberg, who resides in Monte Carlo, held the provisional pole for Sunday's race after making a lap in 1 minute, 15.989 seconds on his first run during the final round of qualifying. While attempting his last lap with less than a minute to go, the German ran wide and had to pull over on to the escape road at the Mirabeau section of the Monte Carlo street circuit.
"I thought it was over once that happened, because I thought the track would ramp up and somebody else could beat the time," Rosberg said. "In the end, I'm really happy that it worked out. To be on the pole at home is fantastic. It couldn't be better."
Lewis Hamilton was making his final run at the same time as Rosberg, his Mercedes teammate, but Hamilton had to slow his pace in the area of Rosberg's incident, as the yellow flags were displayed.
When the Mercedes drivers returned to parc ferme (the enclosed and secure area in the paddock where the cars are inspected), Rosberg celebrated his pole win, while Hamilton looked less delighted with his second-place finish in qualifying. Hamilton's best lap in Q3 was 0.059 seconds behind Rosberg.
Steward said after qualifying had concluded that they were investigating the incident.
Hamilton was on pace to beat Rosberg's time during his final lap before he had to slow for the yellows.
"Yeah, it is ironic," Hamilton said when asked about Rosberg's mishap occurring on the last lap. "It was OK. I was up a couple of tenths [of a second], so It was OK."
Hamilton, who currently holds the lead in the F1 world championship point standings, is attempting to win his fifth consecutive grand prix. Rosberg scored the victory in the season-opener in Australia, but Hamilton has won every race since -- Malaysia, Bahrain, China and Spain. His advantage over Rosberg is just three points.
There has been growing tension between Hamilton and Rosberg during the season, and now it's reached a new height.
"Of course, I'm sorry for what happened to Lewis," Rosberg said. "I didn't know exactly where he was, but once I was reversing, I did see that he was coming up. Of course, that's not great, but that's the way it is."
Hamilton's response to Rosberg's apology? "I don't have an answer to it," he said.
Hamilton had very little to say during his post-qualifying press conference.
Rosberg scored his sixth career pole in Formula One, including his second this season. He started first in the Bahrain Grand Prix but finished second to Hamilton in that race.
The pole sitter for the Monaco GP has won nine of the last 10 races, including the previous five. Rosberg started on pole and led all 78 laps to win last year's event.
Monte Carlo is one of the most difficult circuits on the F1 schedule, with overtaking here virtually impossible.
Daniel Ricciardo from Red Bull qualified third, while his teammate, Sebastian Vettel, the four-time defending world champion, took the fourth spot.
Ferrari drivers Fernando Alonso and Kimi Raikkonen were fifth and sixth, respectively. Toro Rosso's Jean-Eric Vergne placed seventh and Kevin Magnussen from McLaren eighth.
Vergne's teammate, Daniil Kvyat, and Force India's Sergio Perez completed the top-10.