"Tickets will remain valid for the rescheduled performance which will be announced as soon as possible.
"Despite Nicki’s best efforts to explore every possible avenue to make tonight’s show happen, the events of today have made it impossible. We are deeply disappointed by the inconvenience this has caused."
Fans were told of the postponement just after 21:30 BST - around the time she had been expected to come on stage and more than two hours after doors opened.
There were some boos in the arena after the announcement before everyone filed out.
“I'm disappointed because I saw this afternoon that Nicki Minaj got arrested in Amsterdam,” said Kian Young, 23, who had travelled from Scunthorpe.
“So I'm confused as to why the Co-op arena hasn’t spoken to its fans. Why didn’t they cancel it at 17:00?
“Everyone's come - my missus is crying. Why not tell us it's cancelled before bringing us in?”
Olivia Gibson, 21, from Newcastle, said she was now an “ex fan”, and Minaj has a track record of running late and should have allowed more time to travel.
“I feel appalled. But also, in a way, I'm also not shocked,” she said.
“And it's not the Co-op Live’s fault. It's Nicki Minaj’s fault. She’s just let all her fans down.”
Minaj filmed part of her arrest, posting it to social media.
In the video, a police officer can seemingly be heard telling Minaj: "You are under arrest."
The music star posted a series of messages on X, apparently in relation to the incident.
"They took my luggage without consent," she wrote in one. In another she added: "This is Amsterdam btw [by the way], where weed is legal," using a colloquial term for the drug cannabis.
It is technically against the law to possess, sell or produce drugs in the Netherlands. But the country operates a policy of toleration towards the sale or possession of small amounts of some drugs.
The BBC has approached Minaj's representatives for comment.
The first major ticketed exhibition for the Glasgow museum presents the work of Edgar Degas.
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