Tanjug news agency said that the man was Slobodan Vucinic.
His father Blagoje was also arrested and later released in the southern, ethnic Albanian part of Kosovska Mitrovica.
The arrest was carried out by EULEX and KPS members, the news agency is reporting, quoting an "anonymous relative".
EULEX spokesperson Nicholas Hawton confirmed for Tanjug earlier on Thursday that the the EU mission's police had arrested a suspect in the case.
The KPS member, identified as Enver Zumberi, was shot and killed in a firefight on July 26, close to the Brnjak administrative line crossing.
The incident that happened a day after members of the ROSU unit were sent to the line in an attempt of the authorities in Priština to seize both Brnjak and Jarinje checkpoints.