The Elder of Punia, Liudvikas Pociejus, founded a town on the site of Trobos and gave it its present name.

The description of the town in the early 20th century: A rather small town - it used to be much bigger, with as many as thirty inns, market and Magdeburg rights - and now with thatched cottages, with only a few merchants' mason houses in the town centre by the road, and a newly built brick school beside a church.The Molotov-Ribbentrop Pact, signed in August 1939, determined that Liudvinavas, as well as the whole of Lithuania, would be ceded to Germany; but soon after the signing of an additional treaties, almost the entire territory of Lithuania was placed under the influence of the USSR, while Liudvinavas (like Kapčiamiestis and Vilkaviškis) remained in Germany's zone, but was later reclaimed by Stalin.

After the World War II, Lithuanian partisans of the Vytautas Brigade of the Tauras District were active in the area.

On 27 April 1947, the Chief of Staff V. Vabalas (nickname Kunigaikštis) was killed when the Soviet forces surrounded his bunker near Liudvinavas.

The town's coat of arms, granted by King Stanislaus August Poniatowski in 1791, was restored by decree of the President of the Republic of Lithuania in 2001.