"Despite Nicki's best efforts to explore every possible avenue to make tonight's show happen, the events of today have made it impossible," the Co-op Live venue in Manchester said in a post on X.
Minaj, 41, was detained hours before the show had been scheduled to start.
Dutch military police confirmed a 41-year-old American woman had been held for possession of soft drugs on Saturday, adding it was prohibited to take such substances out of the Netherlands.
Police did not identify the suspect, but in a later post on social media platform X said the woman had been fined and released around 7.45pm (GMT).
That was 45 minutes after Minaj had been due to begin performing at the Manchester Co-op Live.
The singer had earlier posted a video on X in which a Schiphol employee apparently told her that police wanted to "search all her luggage".
Another video on her social media showed an officer telling her she was "carrying drugs".
In the video Minaj denies that.
"Now they said they found weed & that another group of ppl have to come here to weigh the pre-rolls," she said in a following post.
The former American Idol judge played a show in Amsterdam's Ziggo Dome on Thursday and was due to return there for another show on June 2.
