"There are about 3,000 people who have left the camp so far," Jenin deputy governor Kamal Abu al-Roub told AFP, adding that arrangements were being made to house them in schools and other shelters in the city of Jenin.
At least six drones could be seen circling over the city and the adjoining camp, a densely packed area that houses around 14,000 people in less than half a square kilometre.
Shahzada Dawood, 48, and his son Suleman, 19, are members of the Dawood dynasty, owners of an industrial empire that is one of the most profitable in Pakistan.
Russia has unleashed regular long-distance missile and drone attacks since October, but it seriously increased strikes in May as Ukraine prepared for a counteroffensive this month.
Some 25 battles had taken place over the past day near the eastern town of Bakhmut, and further south near Avdiivka and Maryinka, all in the Donetsk region, but also near Bilohorivka in the Luhansk region, Ukraine's armed forces general staff said.
Around 600 sq km of Ukraine's southern Kherson region is underwater, 68% of which are located on the Russian-occupied left bank of the Dnipro River, the regional governor also said on Thursday.
Kyiv said the destruction of the dam - seized by Russia in the early hours of the war - was an attempt by Moscow to hamper its long-awaited offensive, which Ukraine's leader stressed would not be affected.