The first stretch of barbed wire barrier will run for about 500 meters (1,640 feet) and measure 1.8 meters (six feet) high, Chief Public Affairs Officer of Defence Staff of Lithuanian Armed Forces Andrius Dilda told Reuters.
The government said the military-style wire coil would cost 4.9 million euros ($5.81 million) to put up and run along most of the frontier, which passes over sparsely populated areas and large stretches of forest and marsh.
At a later date the barrier will be reinforced with a two meter (6.5 ft) high border fence topped by razor wire, costing an additional 41 million euros, the interior ministry said.
Hundreds of migrants have crossed from Belarus in recent days, most of them Iraqi citizens, Lithuania has said.
Belarus in May decided to allow migrants to enter Lithuania in retaliation for sanctions imposed by the bloc after Minsk forced a Ryanair flight to land on its soil and arrested a dissident blogger who was on board.