Uganda says Kony left a hideout east of the Nile two weeks ago and is fleeing towards lawless eastern Congo.
A military spokesman said Ugandan forces attacked Kony's group on Tuesday as it headed for the remote border.
"Our soldiers pursued and caught up with rebels commanded by Kony southwest of Juba and killed four of his bodyguards on the spot," Lieutenant Chris Magezi said in a statement.
"Kony and his defeated remnants are on their way to Democratic Republic of Congo fleeing the offensive."
Magezi said one Ugandan soldier was injured in the clash. It was not possible immediately to verify his report.
Ugandan military chiefs say the LRA leader plans to rejoin his deputy Vincent Otti, who is blamed for last month's murder of eight U.N. peacekeepers in Congo's Garamba National Park.
Operating from Sudanese hideouts in recent years, Kony's guerrilla group has massacred civilians, mutilated survivors and kidnapped some 25,000 children as fighters and sex slaves.
Kony is sought by the International Criminal Court and since the ICC issued arrest warrants in October, Sudan has allowed Uganda troops deeper into its territory in pursuit of the LRA.
The war has uprooted 1.6 million people in northern Uganda alone, and in October the International Criminal Court unsealed arrest warrants for the LRA leaders for war crimes.