A painting personally gifted by Spanish-born master Pablo Picasso to Greece was stolen from Athens' National Gallery early today along with two other important artworks, officials said.

"Woman's Head", a 1939 oil on canvas, had been given by Picasso to the Greek state in 1949 in recognition of the country's resistance to Nazi Germany, the police said in a statement.

"Mill", a 1905 oil painting of a windmill by Dutch abstract artist Piet Mondrian was also stolen, along with a sketch of St Diego de Alcala by 16th century Italian artist Guglielmo Caccia, better known as Moncalvo, the police said.

Authorities said the thief, or thieves, had knocked out the alarm system and forced open a balcony door at the back of the building, which is located across from one of Athens' top hotels.

A guard told police that a burglar alarm went off shortly before 5:00 am and that he saw the silhouette of a person running from the building.

He told police that he ran after the thief, who dropped another Mondrian oil painting, "Landscape", depicting a farmhouse and painted around 1905, according to the gallery's website.

The break-in lasted only around seven minutes.

The police added that the guard had been distracted earlier in the evening by alarms that were triggered at various entry points, but when he went to investigate he found no one in the gallery.

The police said the theft occurred on the final day of an exhibition titled "Unknown Treasures" that included prints and etchings by Duerer and Rembrandt.

The gallery in the centre of the Greek capital planned to close its doors following the exhibition for expansion and renovation work.

It has a vast permanent collection of post-Byzantine Greek art, as well as a small collection of Renaissance works and some El Greco paintings.