Mickey Rosenfeld, a police spokesman, said police swung into action after protesters hurled stones at security men.
He said 16 policemen had been lightly wounded and ten protesters arrested.
Mustafa Suheil, the town's deputy mayor, said 15 protesters had been lightly wounded.
Al Jazeera's Ayman Mohyeldin, reporting from Umm el-Fahm, said a group of about 100 Israeli right-wingers wanted to march in the town, home to about 15,000 Palestinians.
He said the group's march followed a supreme court decision that allowed them to "excerise their sovereignty over the city".
'Provocative decision'
"They wanted to come with Israeli flags and many people thought that was a very provocative decision," he said.
"Police have been using tear gas to try to disperse them. The Palestinians had gathered here to prevent this extreme Israeli right wing-group from entering the town.
"Police feared that there could be a confrontation between the residents and this group."
Mohyeldin said the police were withdrawing and the situation was calming down.
He said police officers and Palestinians injured in the clashes had been evacuated from the scene.
Tensions inside Israel, particularly among the indigenous Arab population, have been extremely high following the war on Gaza, Mohyeldin said.
"And subsequently since then we have been hearing accounts of the conduct of the Israeli forces and that has angered many Palestinians inside Israel as well as peace activists."
He said Palestinians inside Israel were complaining that they were being treated as second-class citizens - deprived of many of the same resources that the predominantly Jewish neighbourhoods in cities of Israel receive.