A Picasso and a Mondrian were stripped from their frames at Greece's biggest state art museum.
A police statement said the burglars who entered through a balcony door also took a pen and ink drawing of a religious scene by Italian 16th century painter Guglielmo Caccia. It said a fourth work by Mondrian also was removed from the National Art Gallery in one of the best-guarded areas of central Athens, but the thieves abandoned it as they fled.
Museum officials were unable to immediately estimate how much the stolen works were worth.
Police said the heist took about seven minutes. The thieves had intentionally set off alarms on several occasions since Sunday evening without actually entering the building, prompting guards to disable at least one.
The burglars still triggered a sensor in the exhibition area, but a guard only got there in time to see a man running off.
Among the stolen works was a cubist female bust by Pablo Picasso, which the Spanish painter had donated to Greece in 1949 with a dedication "in homage to the Greek people" for their resistance to Nazi occupiers during World War II.
The thieves also took a 1905 representational oil painting of a riverside windmill by Mondrian, famous for his later abstract linear works, and a drawing of St. Diego de Alcala by Caccia. All three works were stripped from their frames.
The art gallery contains mostly 19th and 20th century Greek painting, but had just wound up a display of its western European collections that include prints and etchings by German master Albrecht Duerer and Rembrandt van Rijn. It had been due to close Monday for a long period of extension and refurbishment.