The town was first mentioned in written sources in 1402.From the 15th to 18th century, the town belonged to the Radziwiłł family. In 1811 it was bought by Ignacy Baliński, father of historian Michał Baliński. His wife from the Śniadecki family initiated construction of the neoclassical Jašiūnai Manor, designed by architect Karol Podczaszyński. The construction was undertaken between 1824 and 1828. The manor became a cultural center: it was a residence of Jan Śniadecki and Juliusz Słowacki frequently visited by Adam Mickiewicz, Tomasz Zan, Stanisław Bonifacy Jundziłł, Józef Mianowski. This generation of Polish Romanticsstudied and idealized the history and culture of the former Grand Duchy of Lithuania. These studies had great influence on the worldview of the szlachta of the Vilnius Region: they would identify themselves as Poles while remaining loyal to the Grand Duchy.
Alongside cultural life, the manor owners encouraged small industry: a ceramics workshop (still operating as of 2009), a factory of resin and turpentine, brickyard, paper factory.After the Uprising of 1863 and Baliński's death, Jašiūnai lost its position as a cultural center. The valuable library collection was transported to Poland or lost during the wars. As part of the Wilno Voivodeship, Jašiūnai belonged to the Second Polish Republic during the interwar period.
During World War II, Jews were assembled in a building in the Jašiūnai manor and locked there. In September 25, 1941, the Jews of Jašiūnai were shot, together with those from other villages by the Vilnius Special Squad. According to the Jäger Report, 575 Jews were murdered that day: 215 men, 229 women and 131 children. Three Roma people were shot and buried together with the Jews.