Thirteen people were arrested following the melee, including one Klan member who is accused of stabbing a counter-protester with a flagpole, said Anaheim Police Sergeant Daron Wyatt.
Several counter-protesters were taken into custody after stomping a KKK member on the ground, Wyatt said.
Wyatt said the altercation took place as soon as several Klan members arrived at the park about a mile north of Disneyland, for a planned rally there.
"As soon as they got out of their vehicle, immediately they were attacked by counter-protesters and this caused a melee down the block," he said.
Wyatt said four people were wounded in the ensuing confrontation. The person most seriously wounded was stabbed with a flagpole that had an American eagle finial at the top and taken to a local hospital in critical condition.
Several witnesses said that a peaceful counter-protest had been under way for about three hours when the Klansmen arrived in a black SUV.
The vehicle pulled up and three men got out and began to unload signs when the group of about 50 counter-protesters approached them, yelling and throwing sticks, witnesses said.
"Three people were stabbed by the fire hydrant," said Darren Simpson, 49. "These Klan guys were fighting for their lives."
The Klan members attempted to get back into the car, but it sped off, leaving them behind, said Dion Garcia, 37.
He said the angry mob chased the Klansmen down the block, yelling: "Get out of here! You're not welcome!"
"It was crazy," Garcia said. "A lot of us were trying to break it up. This was not necessary, they should've just let the Klan protest. This is America, we have free speech."
The Klan, founded after the abolition of slavery in the U.S. South in the mid-19th century, has evolved in recent years into a collection of loosely affiliated or independent groups that share a political philosophy based on racial separation.
Most recently it made national headlines when a former KKK leader, David Duke, said he backed Donald Trump for the Republican presidential nomination.
Trump rejected Duke's support and on Friday a man wearing a shirt reading "KKK endorses Trump," was ejected from a Trump campaign rally in Oklahoma.