The singer was due to perform a show in Britain later Saturday and posted images on social media of her being questioned by officials.
Police confirmed to AFP that they had detained a 41-year-old American woman but declined to confirm directly that it was Minaj, as per their usual policy.
"We never confirm the identity of a person in custody but I can confirm we have arrested a 41-year-old woman suspected of trying to export soft drugs to another country," Robert Kapel, a military police spokesman, told AFP.
Kapel later told AFP the suspect had been released after the payment of a "reasonable" fine.
"There's no reason for us to keep her in custody any longer. We have all the information for our file. Case closed," he told AFP.
The rapper posted on X that authorities told her they had found cannabis in her luggage, which she said belonged to her security personnel.
"Keep in mind they took my bags without consent. My security has already advised them those pre-rolls belong to him," she wrote on X, referring to marijuana joints.
"Now they said I have to go five mins away to make a statement about my security to the police precinct," she said. "It's to try to make me late so that they can write negative stories."
A common misconception outside the Netherlands is that dope is legal in the country, home to world-famous coffee shops (which actually sell pot) that are a huge draw for cannabis smokers.
The consumption of small quantities of cannabis is technically illegal but police choose not to enforce the law as part of a "tolerance" policy in place since the 1970s.
Transporting the drugs to another country is illegal.
'Sabotage'
Minaj's profanity-laced lyrics, skin-baring videos and unique, animated flow catapulted her to fame in 2010.
Known for a bold sartorial style that includes neon costumes and wigs, Minaj -- whose hits include "Starships," "Bang Bang" and "Anaconda" -- is considered one of rap's most influential female artists.
She was due to perform in Manchester on her Pink Friday 2 World Tour, and the hashtag #FREENICKI was trending on X.
It was not immediately clear whether the performance would go ahead.
"They've been trying to stop me from coming to every show," she posted on her Instagram account.
"This is what it looks like when ppl (people) are paid big money to try to sabotage a tour after all else failed," Minaj said.
Her brash personality and penchant for controversy have also made Minaj a tabloid regular, in particular a feud at a Fashion Week 2018 after party that saw rap rival Cardi B throw a shoe and allegedly attempt to fight Minaj.
The rapper also hit the headlines during the Covid pandemic after skipping New York's star-studded Met Gala because of its requirement that attendees be vaccinated.
She said she would get the jab only once she had "done enough research".
She said a friend of a cousin in Trinidad had experienced swollen testicles after getting the vaccine -- claims that sparked a formal rebuttal from the Caribbean nation's health minister.
