A police spokesperson identified the suspect as the same man who stabbed three people at the parade in 2005.
Yishai Schlissel, an ultra-Orthodox Jew, was sentenced to 12 years in prison for that attack and was released from prison three weeks ago.
Two of the injured are in a serious condition, the city’s ambulance service said.
According to eyewitnesses, the attacker emerged behind the marchers and began stabbing them while screaming, before being tackled by a police officer.
Some photo shots capture the man as he reached for the knife from inside his coat before raising the knife above his head.
He ran into the gathering and began stabbing some of the marchers.
The parade continued after the wounded were taken to a hospital, with protesters chanting “end the violence”.
Israeli Prime Minister Benjamin Netanyahu said the attack contradicted the country’s “basic values”.
Additional information from BBC