Dozens of the approximately one thousand away supporters in Hungary's grandstand section attacked some crowd hosts who were forced to back down before the police came to the rescue with batons.
The quarrel lasted for several minutes before order was restored.
A supporter has been arrested on suspicion of violating public order with racist motives.
The reason for the criminal classification is comments to an audience host.
Despite the unrest, the match was not interrupted but continued and was played according to plan.
Hungary took the lead after a penalty goal by Roland Sallai in the 24th minute and the home side's midfielder John Stones equalized in the 37th.
Albania's match against Poland in Tirana in the same qualifying group was also surrounded by unrest.
Bottles were thrown in from the home crowd against Polish players who celebrated Karol Swiderski's 1-0 goal in the 77th minute.
The match was interrupted but resumed and ended 1-0 to the away team.
Poland thus keyed in on England, who still have a firm grip on first place in qualifying group E and the direct place in the World Cup finals in Qatar next year.
With two games left, England leads the group by 20 points, three ahead of second-placed Poland by 17.