The EU announced travel bans and asset freezes on two South Sudanese military leaders on Thursday but did not name them at the time. The other officer named on Friday was Santino Deng, a commander of the third Infantry Division of the government army.
The EU said Gadet had been in charge of a militia during a three-day assault on an oil town in northern Unity State.
Fighting erupted in Juba in December between the government forces of President Salva Kiir and supporters of Riek Machar, his former deputy and long-time rival. The conflict has revived deep ethnic tensions in the world's newest country, which won independence from Sudan in 2011.
Peace talks between Kiir and Machar stalled after they agreed a truce. The U.N. estimates more than 10,000 people have been killed and about a million displaced.