Referee Martin Atkinson was forced to call a halt to the Group I match at Stadion Partizana following a pitch disturbance towards the end of the first half, with the score reading 0-0.
A drone flew over the ground, carrying a flag featuring Albanian national symbols.
Serbia defender Stefan Mitrovic jumped to bring the flag down and an unsavoury melee between players from both sides soon escalated as a number of supporters entered the field of play.
Following an initial suspension of play and the deployment of riot police around the pitch, the match was abandoned.
A short statement from European football's governing body confirmed an investigation would take place.
It read: "The UEFA EURO 2016 Group I qualifying match between Serbia and Albania in Belgrade was abandoned and the circumstances will be reported to the UEFA Control, Ethics and Disciplinary Body."
Tuesday's contest was set against a backdrop of political tensions between the two countries.
Serbia refused to allow Albanian fans to attend the match, with the Albanian Football Association's (FSHF) request for 2,000 tickets met with an insistence that tickets should be sold to Albanian passport holders only.
That condition, which was rejected by the FSHF, would have excluded the residents of Kosovo, which is heavily populated by Albanians but not recognised as a sovereign state by Serbia despite its declaration of independence in 2008.
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