Video footage showed the fans flailing wildly on the street and hitting each other with belts and sticks for several minutes.
The clash added to outrage in Israel over rising soccer violence that resulted in the abandonment of Monday night's game between local rivals Maccabi Tel Aviv and Hapoel Tel Aviv.
Police spokesman Micky Rosenfeld said six people were arrested following Tuesday's street fight. He said police would be reviewing footage of the game and courthouse brawl and further arrests were expected.
Maccabi and Hapoel were level at 1-1 in the first half when a shirtless fan ran onto the field and began hitting and kicking Maccabi midfielder Eran Zehavi.
The Hapoel fan, who authorities later said had been arrested 11 times for acts of violence, crossed the goal line and kicked Zehavi after he had levelled the score with a penalty kick.
The fan then taunted the Hapoel bleacher section by simulating gunshots toward them.
Zehavi retaliated with a shove to the throat before the fan, 41-year-old Alroee Yadai, swung a fist toward his head.
The two exchanged more kicks, with Zehavi landing a flying karate kick, before security and other players intervened. The fan was dragged away.
The referee then showed Zehavi a red card, sparking screaming between players and coaches.
The game resumed for a few minutes before more fans ran onto the field and began exchanging blows with security personnel.
The game was then halted and the players came off as debris descended from the stands toward Zehavi, as he left the field with his coach, Jordi Cruyff. Police arrested 12 fans.
Former Israel international and current Hapoel coach Eyal Berkovic called it a "black day" for Israeli soccer.
"This is not soccer, this is war," Berkovic said.
A special parliamentary committee has convened as a result of the brawl.
"What happened was extremely serious and shameful," Israeli Culture and Sport Minister Limor Livnat said. "It's a shame there are those who want to turn the field into a battle zone and spoil the principles of Israeli soccer and sport."