Two of the wounded people had serious injuries, the ministry said in a statement on Tuesday.
Witnesses stated that a house was besieged by the Israeli troops and hit with rockets. Footage circulating on social media showed helicopters over a column of military vehicles entering the city.
Israeli authorities claimed one of the Palestinian men they killed was behind the shooting of two brothers from an illegal settlement near the Palestinian village of Huwara last week.
Israeli Prime Minister Benjamin Netanyahu’s office announced troops had “eliminated” the gunman who last month killed two Israeli settlers in the West Bank.
The army entered a building in the Askar refugee camp and arrested three men, including two sons of a 49-year-old man killed in Jenin.
On Tuesday night, thousands of Palestinians emerged across the occupied West Bank in protest.
Nabil Abu Rudeineh, spokesman for Palestinian President Mahmud Abbas, called the use of rockets in Jenin on Tuesday an act of “all-out war”.
Abu Rudeineh accused the Israeli government of being “responsible for this dangerous escalation which threatens to inflame the situation and destroy all efforts aimed at restoring stability”.
A general strike is being observed across the occupied West Bank. Businesses in cities including Jenin, Nablus and Ramallah shut their doors on Wednesday morning in response to the killings.
There has been no sign of any let up in the violence, ahead of the start of the Muslim holy month of Ramadan and the Jewish Passover festival.
Settlers have killed at least five Palestinians in 2023 so far, while Israeli forces have killed at least 68 Palestinians this year.