The painting, entitled Ballerina adjusting her slipper, was taken on Monday from the home in the island’s second largest city, Limassol, and was not insured, a police spokeswoman told AFP.
Art theft is rare in Cyprus and it is believed to be one of the most valuable paintings ever stolen on the Mediterranean island.
The thieves also made off with other items—seven gold watches and three gold opera glasses—worth a total of 157,000 euros ($200,000).
Police said they had arrested a 44-year-old Greek Cypriot in connection with the case and were seeking two other suspects—a South African and a Russian. It is believed the trio knew the victim.
Degas (1834-1917) is regarded as one of the founders of Impressionism.
The French artist is famous for his paintings, sculptures and drawings, more than half of which depict dancers.
The painting is 61 x 47 centimeters (24 x 18.5 inches).
It is one of a number of studies that Degas made between 1873 and 1874 of dancers adjusting their shoes, shown in different poses and from different angles.
ADDITIONAL IMAGE OF NOTE