Another was thrown later in the session but landed on the grass and did not disrupt the action.
Verstappen is running away with the championship, already 93 points clear at the top after 14 of 22 rounds, and the race is sold out for the Red Bull driver's first home grand prix as champion.
The boisterous Dutch fans usually create a party atmosphere at the seaside circuit, but their habit of lighting smoking orange flares has caused problems.
"To hold flares, it’s nice but of course there’s a limit to how much. But to throw it on the track is just stupid," Verstappen told reporters after taking pole position.
"Just don’t do that. It’s not good for anyone -- you get thrown out, so you can’t see the race, and for us the session is stopped because it is dangerous, there’s stuff on the track, so you shouldn’t do it."
The governing FIA said security had removed the person who threw the flare.
Ferrari's Charles Leclerc and Carlos Sainz, second and third in qualifying, also spoke out.
"It’s dangerous, so don’t do these type of things," said Leclerc.
"I don’t know exactly when it was thrown, but if a car is passing at that time it can create unnecessary risk, so hopefully it won’t happen again."
Sainz said fans should be told when flares were acceptable.
"I think it was good that they used them on the in-lap (returning to the pits) when Max took pole but not in the middle of the race or lap one...at 300kph, you don’t want this kind of distraction from smoke," said the Spaniard.
Flares have also been let off at other races in recent seasons, notably in Austria -- Red Bull's home race where a lot of Verstappen fans are also in attendance -- Belgium, Mexico and Italy.
See the qualifying results from the Dutch Grand Prix on Flashscore
