Belgian authorities confirmed that the ambassador had killed himself.
"It was indeed a suicide," said Ine Van Wymersch of the Brussels prosecutor's office. She said no further investigation was planned.
A former author and activist opposed to the authoritarian regime of Serbia's former strongman Slobodan Milosevic, Milinkovic was outgoing, had a warm sense of humor and worked to keep good ties with ambassadors from other ex-Yugoslav countries, according to diplomats and acquaintances.
The diplomats, who spoke on condition of anonymity because they were not authorized to release details, said they knew of no circumstances private or professional that would have prompted him to take his own life.
But Milinkovic, 52, had mentioned to colleagues at diplomatic functions that he was unhappy about living apart from his wife, a Serbian diplomat based in Vienna, and their 17-year-old son.
One of the diplomats described his death to The Associated Press, saying she had spoken to a member of the delegation who had witnessed the leap from the 8- to 10-meter-high (26- to 33-foot-high) platform.
The diplomats all spoke on condition of anonymity because they are not permitted by foreign service regulations to speak publicly to the press.
The death cast a pall on the second day of a meeting of NATO foreign ministers. Officials said they were shocked by the news of the death of a very popular and well-liked man.
NATO's Secretary General Anders Fogh Rasmussen said he was "deeply saddened by the tragic death of the Serbian ambassador."
"As Serbian ambassador to NATO he earned the respect and admiration of his fellow ambassadors," he said.
When Yugoslavia was a united country, Milinkovic worked for a prominent Yugoslav foreign policy think-tank. But when Milosevic seized power in Serbia in late 1980s, Milinkovic joined other liberals who opposed the former strongman's regime and presented a rare voice of moderation during the era when much of Serbia was engulfed in nationalist fervor. He established close ties with international human rights and other groups and remained active in anti-war groups.
After Milosevic was ousted in 2000, Milinkovic was appointed Serbia's ambassador to the Organization for Security and Co-Operation in Europe, or OSCE, in Vienna.
He was transferred to NATO as Serbia's special representative in 2004. Serbia is not a member of the military alliance, but Milinkovic was named ambassador after Belgrade joined NATO's Partnership for Peace program, which involves neutral states.
The move to join the NATO program had angered Serbian nationalists who are now in power. They have pledged that Serbia will never join NATO because of the alliance's 1999 bombing campaign that forced Milosevic's forces to withdraw from Serbia's southern province of Kosovo. In 2008, Kosovo declared independence from Serbia, which has never accepted that loss.
Milosevic was widely blamed for instigating the '90s Balkan wars that followed the breakup of Yugoslavia, conflicts that claimed more than 100,000 lives and left millions homeless.
At NATO, Milinkovic worked to foster closer ties with the representatives of all five other nations that gained independence after the bloody 1991 breakup of the former Yugoslav federation into Bosnia, Croatia, Macedonia, Montenegro, Slovenia and Serbia.
Relations were still politically charged when Milinkovic first arrived in Brussels, but they have since improved drastically.
Two months ago, when Croatia's ambassador to NATO was being transferred to Moscow, Milinkovic organized a dinner for all five of his counterparts and a band played music from all parts of the former Yugoslav federation.
He is survived by his wife and son.