Police said the attack was politically motivated.
Witnesses said the minibus was travelling through the city of Petach Tikva when the attacker stood up and began stabbing passengers.
One witness, giving his name as Benny, said: "He jumped on people and started to stab them. Police ran after him and caught him ... There are lots of blood stains on the road."
Other witnesses said an angry crowd subdued the man on board the yellow bus before police took him away.
"They pummelled him. It was a great mess," a witness, identified as Moshe, told Israel Army Radio.
Police said one woman was killed. Israel's national rescue service said four other people were wounded, three of them women, and all were in moderate to serious condition.
Police said the attack was politically motivated, but gave no further details. They said the attacker came from the West Bank, but it was unclear how the man had entered Israel.
There was no immediate claim of responsibility.
Tensions between Israel and the Palestinians have risen in recent days after Israel killed a top commander of the Islamic Jihad militant group.