The January increase came mainly from industries of transport equipment, iron and steel, communication electronics equipment as well as commodities such as metal oxide semiconductor ICs, large passenger cars and transmission and control parts.
In December, the output was up 2.5 percent from November.
The Ministry of Economy, Trade and Industry on its website said the January figures suggest the slump in output has bottomed out and show some signs of picking up.
The ministry said production and shipments increased in January, while inventories and inventory ratio decreased. Output was expected to increase in February and March.
Japan currently remains under recession.
The new government of Prime Minister Shinzo Abe, which took over in December after its party won a landslide victory in parliamentary elections, has as its top priority bringing Japan out of its chronic deflation and kick starting the economy, which is has been hit by declining exports and a weak domestic demand.