Thieves broke into the gallery in the early hours and snatched Picasso's 1939 painting Woman's head, donated to the Greeks by the artist in 1949, and Mondrian's Mill dated 1905, police said.
They also took a sketch by Italian painter Guglielmo Caccia, which was donated to the gallery in 1907.
"It all happened in seven minutes," said a police official who declined to be named.
To mislead the guard, the thieves activated the gallery's alarm system several times before breaking into the building at 4:30 a.m (0230 GMT). The guard turned off the alarm only to later spot one of the thieves through the motion detector.
Before escaping, the thief dropped another 1905 Mondrian painting, the Landscape, police said.
It was not clear how many people were involved in the theft. Police were looking for suspects and the art in Greece and abroad.
In October, police in Serbia recovered two paintings by Picasso stolen in 2008 from a gallery in Switzerland and worth millions of dollars.
Greece recovered in September a painting by Flemish master Peter Paul Rubens stolen from a museum in Belgium in 2001 and arrested two Greeks who tried to sell it to undercover police for about 1 million euros.
-Reuters
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