The suspect has been identified as a former pupil of the British School, which has a site in neighboring Voorschoten.
More than 20 schools were told to stay closed on Monday in Leiden in response to the threat posted on internet forum 4chan.
The anonymous writer said they would shoot their teacher “and as many students as I can”.
He or she said they would be carrying a 9 mm Colt Defender gun and a note “which will explain why I did it”.
The threat was picked up by Swiss police during internet checks at the weekend, Dutch media report.
Dutch police said on Monday morning that some 22 secondary schools – covering the 12 to 16 age group – had been closed for the day.
Some schools, such as the Da Vinci College and Driestar College, had police officers outside them.
Following reports of an arrest, the British School in the Netherlands issued a statement saying: “We have been informed that a former student… has been arrested in connection to threats made against a Dutch school in Leiden.”
The school said the suspect left its senior school in October 2011 as a result of inappropriate behavior, Dutch broadcaster NOS reports.
The British School in the Netherlands has four schools based in and around The Hague. The senior school site is based in Voorschoten, close to Leiden.
Earlier Leiden Mayor Henri Lenferink said the decision to close the schools had been taken because police had not been able to immediately establish the perpetrators of the threat following the tip-off from Zurich.
“It could just be a morbid joke but we don’t want to take any risk,” Henri Lenferink told Dutch broadcaster NOS.
But some questioned the police decision to close the schools, which affected thousands of students.
“Every idiot who sticks a threat on the internet can paralyze half of society,” said Ton Duif, chairman of head teachers’ association AVS.
Leiden lies some 13 miles north-east of The Hague, and is home to the Netherlands’ oldest university.
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