Skirmishes broke out near the National Arena with rival fans throwing fireworks, missiles and smoke bombs at each other while Hungarian "ultras" destroyed the buses they were in because their national flag was wrongly printed on the info guide they received.
There was an electric atmosphere at the stadium, with both teams' vociferous fans creating a deafening roar and letting off dozens of firecrackers and flares shortly before kickoff.
Tempers boiled over throughout the eagerly-anticipated encounter, with fans warned by the stadium announcer about their behaviour on several occasions and riot police spraying tear gas.
Romanian football federation (FRF) president Razvan Burleanu criticised riot police action during clashes with fans, describing it as "unjustified violence".
"The FRF condemns violent and unreasonable treatment of the supporters," Burleanu said in a statement.
"There have been unacceptable and intolerable things, I apologise to the fans who have suffered from (police) abuse."
Hungarian supporters set several seats on fire when Adam Szalai had a goal disallowed for offside six minutes before the break of the tense affair.
Police spokeswoman Irina Dragan said five of the arrested Romanians have been banned from soccer stadiums for one year, adding that nearly 12,000 police and security forces were deployed in and around the stadium.
Local media said 46 people have been injured in clashes at and around the National Arena with 12 taken to hospital due to serious injuries.
The fixture has a long history of crowd violence.
Off the field, the Danube neighbours have a volatile coexistence stemming from Romania's annexation of Transylvania after World War I.
Hungarians are the largest minority in Romania and a large number of Romanians speak Hungarian, especially in Transylvania.
Crowd trouble also marred the Euro 2016 qualifier between Balkan rivals Bulgaria and Croatia, played in Sofia, just south of the Danube, raising fears that could trigger another punishment for the Bulgarian football authorities.
The match at the Vasil Levski stadium, which Croatia won 1-0, was interrupted for a few minutes midway through the first half as rival supporters threw fireworks at each other and flares were hurled from the stands.
Bulgarian Football Union president Borislav Mihaylov, who is also a UEFA executive committee member, said he would not be surprised if European soccer's governing body punished his team for the crowd disorder.
