Former NBA campaigner Fernandez, who played for the Portland Trail Blazers and Denver Nuggets, was allegedly attacked by Zalgiris fans as Real were boarding their team bus after a 105-104 overtime win.
"Real Madrid has reported the incident and is preparing all documents concerning an alleged aggression by fans against Rudy Fernandez," the competition's ruling body said on its website.
"Euroleague Basketball has asked Zalgiris Kaunas to provide its own official reports of the incidents, including details of its security procedures.
"The reports of both teams plus additional information from sources such as the Kaunas police will be forwarded to the Euroleague Basketball Disciplinary Judge for immediate investigation."
Fernandez had scuffled with several Zalgiris players during Real's equally dramatic 75-74 home win over the Lithuanians in January and scored 11 points in Thursday's rip-roaring encounter.
Real, who have won Europe's elite basketball club competition a record eight times, will reach this season's quarter-final playoffs with four games to spare in the second group stage if Panathinaikos Athens beat Spaniards Unicaja Malaga later on Friday.