Many of those at the Sunday night rally in Belgrade were young people, some not even born during Bosnia's 1992-95 war. Dozens of those detained by riot police wearing helmets, protective gear and shields were minors.
The Serbian Radical Party, whose leader is on trial in The Hague, brought in supporters by bus from across Serbia to rally for Mladic. Many came straight from Sunday soccer matches.
During the violence, 32 police and 11 protesters were hurt, and five cars and six shops also suffered damage, police said.
Mladic, indicted for genocide in the 43-month siege of Sarajevo and the massacre of 8,000 Muslims in Srebrenica during the war, was arrested on Thursday in a village 100 km (60 miles) northeast of Belgrade after 16 years on the run.
A Belgrade court ruled on Friday he was fit enough to face genocide charges at the International Criminal Tribunal in The Hague and has served extradition papers.
His lawyer Milos Saljic has said he would appeal the extradition ruling on Monday.
Mladic's arrest is key to Serbia's bid for European Union candidacy and came just weeks before U.N. chief war crimes prosecutor Serge Brammertz was due to brief the U.N. Security Council on Serbia's progress in the hunt for Mladic.
Mladic's wife and son, who live in Belgrade, are expected to visit him in prison again on Monday. At the Sunday rally, Darko Mladic said his father was a defender of his people.
"Ratko Mladic is not a criminal, he did not order the killings. He defended his people in an honorable, fair and professional manner," he told protesters.
Many Serbians agree and admire Mladic as a dedicated military man who did not seek to enrich himself during the war. But others were glad to see him arrested so that Serbia can distance itself from its international pariah status of the 1990s.
"The whole nation of eight million was being held behind because of the fate of one man, that is not right," said a Belgrade taxi driver. "Mladic should have given himself up long ago so we did not suffer this fate."
The Mladic family and lawyer maintain the former general is mentally unstable and thus too ill to face trial.
In Bosnia, Mladic's supporters rallied on Sunday in the eastern town of Kalinovik where he spent his childhood.