The 18-year-old, who won in Spain on his Red Bull debut, will start Sunday's race from the last row of the grid after crashing at the swimming pool exit in the first phase of qualifying.
Australian team mate Daniel Ricciardo, who had the benefit of an upgraded power unit, took pole position.
"It was pretty simple. I turned in slightly too early, touched the inside barrier and broke the track rods. I couldn't steer any more so I went straight into the barrier," Verstappen said.
The shunt scattered debris across the track and brought out the red flags.
"It was all coming together but then into the chicane maybe I underestimated the grip I had," he added.
The driver, whose calm has impressed many in the sport, said the accident was typical for the track, where success and failure are measured in millimetres as well as fractions of a second.
"These things happen, especially in Monaco. If you count the crashes over the last few years, there have been quite a few. Unfortunately, it happens to me in qualifying after a win in Barcelona," he said.
"It was very unexpected from my side. Of course, it is not ideal, but I also try to stay out of the barrier and I don't do it on purpose."
The weather, hot on Saturday with blue skies, could help on Sunday if rain sweeps in as some forecasts are predicting, but he recognised starting 21st would be a challenge on a track where overtaking is extremely difficult.
"It will be very tough but I won’t give up. The car is great, we just have to find a way to get past the people in front," said Verstappen.
Team principal Christian Horner said the crash was "desperately unlucky".
"It's a reminder in this sport of how fine the margins are. We'll be expecting something a bit special from him tomorrow," he told Sky Sports television.
Verstappen also crashed in last year's race at the tricky Sainte Devote corner in his debut season with Red Bull's junior team Toro Rosso.
In that incident, he smashed into the back of Romain Grosjean's Lotus at speed.
(Editing by Ed Osmond)
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