Paintings by Picasso, Matisse, Gauguin, Meyer de Haan, Lucian Freud and two by Monet were stolen on Tuesday from a gallery in Rotterdam in what will rank as one of the most spectacular art heists of modern times.

The dawn raid at the Kunsthal museum in the Netherlands' second largest city was described by police as a well-planned and bold operation. Security experts speculated that the thieves might have taken advantage of Rotterdam's port – one of the largest in the world – to swiftly move the paintings abroad. While police were reluctant to put a price tag on the stolen paintings, experts said it ran into tens of millions of pounds.

One security expert described the museum, designed by the star Dutch architect Rem Koolhaas, as a "gem of a gallery", but a "nightmare to protect", and suggested that thieves spent months plotting the robbery.

The works were named by the museum's management on Tuesday afternoon, as Pablo Picasso's Harlequin Head; Henri Matisse's Reading Girl in White and Yellow; Claude Monet's Waterloo Bridge, London, and Charing Cross Bridge, London; Paul Gauguin's Girl in Front of Open Window, De Haan's Self-Portrait and Freud's Woman with Eyes Closed. The Picasso was the best known work.

Jop Ubbens, the general director of Christie's in Amsterdam, told the Dutch daily newspaper De Volkskrant the paintings were worth "far more than just a few million euros".

He declined to give a more exact estimate, saying he had not seen the paintings. "They could be worth €50m or more," he said, pointing out that a work of Monet's brought almost €52m at auction four years ago, the highest amount ever paid for a French impressionist painting.

Ubbens did not rule out that the paintings had been "stolen to order" by an art collector, "in which case they could be hanging on a wall somewhere by now, never to be seen again."

Alternatively he said, they might have been stolen for ransom. "For example, the thieves might ask for a million euros for the return of the Matisse," he told the paper. He said the idea that the thieves would try to sell the paintings on the open market was unlikely. "That would be a really stupid idea. They are so well known, no one would touch them," Ubbens said.

The works were immediately listed on the Art Loss Register which helps trace stolen works of art, and makes the chance of selling them on harder.

Ubbens said the De Haan was the least well-known work, but suggested that as it resembled a Matisse, "it might have been stolen by mistake".

The works were showing as part of an exhibition at the Kunsthal opened to mark its 20th anniversary. Called Avant-Gardes, the exhibition, which opened just over a week ago and was due to run until 20 January, consisted of 150 works from the Triton Foundation Collection, a collection assembled by the Cordia family which made its money in oil and shipping and is ranked among the richest families in the Netherlands.

The gallery's curators described the exhibition as the first public showing of the "carefully and lovingly assembled Triton collection", which had developed an "international reputation" and comprised "representative works by the most important and influential artists of the late nineteenth century to the present day".

It also includes works by Piet Mondrian, Marcel Duchamp, Vincent van Gogh, Georges Braque and Willem de Kooning.

The gallery was closed until further notice as forensic experts scoured it for clues about the thefts. A short message on the gallery's website informed visitors: "Due to the theft which occurred in the Kunsthal Rotterdam last night, the Kunsthal is closed to the public today."

Security expert Ton Cremers said that it had become easier than ever for thieves to steal paintings even from well-protected galleries like the Kunsthal. He said some of the fault lay with its design.

Calling the Kunsthal a wonderful museum, it was a nightmare from a security point of view: "As a gallery it is a gem. But it is an awful building to have to protect. If you hold your face up to the window at the back you have a good view of the paintings, which makes it all too easy for thieves to plot taking them from the walls," he told De Volkskrant.