The thieves got in through the roof early on Saturday, Dutch police spokesman Remco Gerretsen told BBC News Online.
The stolen paintings are well known to art lovers: View of the Sea at Scheveningen and Congregation Leaving the Reformed Church at Nuenen. Both from the artist's early period, they were executed in 1882 and 1884, respectively.
Police have not yet put a value on them. But Van Gogh's later works have sold at auction in recent years for tens of millions of dollars.
The museum, in the heart of Amsterdam, contains the world's largest collection of Van Gogh works. It holds more than 200 paintings and 500 drawings by the Dutch post-Impressionist.
Museum closed
The theft was discovered at 0800 (0600 GMT) - two hours before opening time - and police cordoned off the museum.
It was reopened later on Saturday, after workers had redecorated the spot where the theft took place.
A museum spokeswoman said the paintings had been taken from the main exhibition hall.
It is the second major theft in the Netherlands in a week. On Monday, thieves raided a diamond exhibition at the Museon in The Hague, making off with gems worth about $5m.
Most expensive Van Goghs
Portrait of Doctor Gachet - sold for $82.5m
Self-portrait - sold for $71.5m
Irises - sold for $49m
Investigators are baffled by the Van Gogh theft, as guards patrol the premises at night and there is tight security inside, including infra-red systems and cameras.
Police found a broken window one storey above street level, a rope and a 4.5-metre (15-foot) ladder leaning against the rear of the building, the Associated Press reported.
Broken glass and a large cloth that may have been used in the burglary were taken away for inspection.
Mr Gerretsen said that so far investigators had found nothing wrong with the museum's security systems. They are examining a security video.
Van Gogh was born in the Netherlands in 1853 and died in France in 1890.
Dutch scenes
View of the Sea at Scheveningen shows a foaming, stormy sea and thundery sky, executed on the spot at the beach resort near The Hague in 1882.
The artist fought against the elements, as the gusting wind embedded grains of sand in the wet paint.
The small canvas called Congregation Leaving the Reformed Church at Nuenen was painted at the beginning of 1884. It is said to have been intended for Van Gogh's mother, but also partly for his father, who had become a pastor at the church in 1882.
Van Gogh lived with his parents in Nuenen, in the Brabant region of the Netherlands, from late 1883 to November 1885, when he moved to Antwerp in Belgium. In Nuenen he focused on scenes of peasant life.
Van Gogh, who committed suicide in France in 1890, is widely considered the greatest Dutch artist after Rembrandt.