It is believed to be the first time since the second intifada - a major Palestinian uprising from 2000 to 2005 - that several Palestinian cities have been targeted simultaneously in this way.
Palestinian reports say that the main roads into Jenin have been closed off with armed clashes in the city’s refugee camp.
An Israeli air strike is said to have targeted a vehicle in a nearby village at dawn.
Israeli forces are said to have entered a hospital in Jenin and blocked off two in Tulkarm.
Israeli military raids of Nablus are reportedly focused on two refugee camps there.
In Far’a camp near Tubas, medics say ambulances are struggling to reach the wounded after an Israeli drone strike.
Foreign Minister Israel Katz said that the Israeli Defense Forces (IDF) have been "operating with full force since last night in the Jenin and Tulkarm refugee camps to dismantle Iranian-Islamic terror infrastructures established there".
He accused Iran, which backs the armed groups Hamas and Palestinian Islamic Jihad, of seeking to open what he called a new front against Israel in the West Bank.
"We must deal with the threat just as we deal with the terrorist infrastructure in Gaza, including the temporary evacuation of Palestinian residents and whatever steps are required," he added.
The Israeli military has given few details but said in a statement that the IDF, internal security agency Shin Bet and Israel Border Police forces were "currently conducting a counterterrorism operation to thwart terror in Jenin and Tulkarm".
