Haneen Zoubi, a parliament member who has become a national hate figure in Israel and received hundreds of death threats since her participation in an aid flotilla to Gaza in the summer, was among those hurt.
Ms Zoubi reported being hit in the back and neck by rubber bullets as she fled the area when police opened fire. In an interview, she said she believed she had been specifically targeted by police snipers after they identified her.
Police denied her claims, saying they had used only tear gas and stun grenades.
Some 1,500 police were reported to have faced off with hundreds of Arab and Jewish demonstrators in the town yesterday.
Shimon Koren, the northern police commander, admitted special paramilitary forces had been used against the Arab counter-demonstration, as well as an undercover unit more usually deployed at Palestinian protests in the West Bank.
An officer disguised as an Arab demonstrator, from the so-called "mistarvim unit", was among the injured, apparently after police fired a stun grenade at him by mistake.
Ms Zoubi harshly criticised the police violence. "The police proved that they are a far more dangerous threat to me and other Arab citizens than the fascist group that came to Umm al-Fahm," she said.
The march was organised by far-right settlers allied to Kach, a movement that demands the expulsion of Palestinians from both Israel and the occupied territories. The movement was formally outlawed in 1994, but has continued to flourish openly among some settler groups.
The organizers said they were demanding the banning of the Islamic Movement, which has its headquarters in Umm al-Fahm.
The Islamic Movement's leader, Sheikh Raed Salah, has angered Israeli officials by heading a campaign in Jerusalem's Old City to highlight what he says is an attempted Israeli takeover of the Haram al-Sharif compound that includes the al-Aqsa mosque.
He was also on the Mavi Marmara aid ship to Gaza in May, and claimed at the time that Israeli commandos had tried to assassinate him. Nine passengers were killed, some of them by close-range shots to their heads.
The sheikh is currently serving a three-month jail sentence over clashes with the Israeli security forces close to the al-Aqsa mosque.
Michael Ben Ari, a former Kach member and now an MP with the rightwing National Union party, who attended the march, said Israel must not be a "stupid democracy and let people who want to destroy us have a voice".
Baruch Marzel, one of the march organisers, told Israel Radio: "If the Kach Party was outlawed, then the Islamic Movement deserves to be outlawed 1,000 times over."
On hearing of Ms Zoubi's injuries, he added: "It was worth going to Umm el-Fahm. She is our enemy."