Seán Rooney: Arrest made after Irish soldier killed in Lebanon
Several arrests were made, Qazet.az reports citing the influential pan-Arab newspaper Asharq al-Awsat.
According to AFP news agency, quoting an unnamed security source, the prime suspect was handed over by the powerful Hezbollah militant group.
"The main shooter has been arrested by security forces after Hezbollah handed him over hours ago," the source said.
Hezbollah has denied any involvement in the shooting. It is not clear whether the suspect is a member of the militant group.
The village where Pte Rooney was killed is a stronghold of the Iranian-backed Hezbollah movement.
Three separate investigations are being conducted into the incident by the UN Interim Force in Lebanon, Lebanese authorities led by a military prosecutor and the Irish Defence Forces.
It is understood the vehicle was surrounded by a mob and fired on while travelling to Beirut at about 21:00 on 14 December.
Pte Rooney was repatriated to Ireland last Monday following a UN ceremony to honour him in Beirut the previous day.
Irish President Michael D Higgins and Taoiseach (Irish prime minister) Leo Varadkar were among mourners present at Pte Rooney's funeral service in County Louth on Thursday.