"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.

The back of the painting reads in French "for the Greek people, a tribute by Picasso" according to a photograph released by police.

"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.

"I am very sorry because an artwork of huge value was stolen," Citizen's Protection Minister Christos Papoutsis told reporters, referring to the Picasso.

Papoutsis termed the gallery's security arrangements "non-existent" and noted that a private security company hired to supplement the building's sole guard "took hours" to respond to the break-in.

"This incident should prompt a re-evaluation of the National Gallery's security arrangements," Papoutsis said.

The authorities did not specify the value of the artworks stolen, but Skai television said they were worth about 5.5 million euros ($7 million).

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.

The gallery was on reduced security staffing owing to a three-day strike.

The sole 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.

"I don't know if we can say it was an inside job, but they were certainly professionals," police spokesman Thanassis Kokkalakis told AFP.

"They provoked false alarms to gauge the guard's response time," he said.

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. (AFP)