A woman working as a health support staff member was wounded by gunshots to the chest and abdomen,
The ministry of health named the man as Mostafa Al Kastoni. Militant group Jenin Brigades claimed Al Kastoni as one of its fighters and began funeral processions on Thursday afternoon.
One unnamed eyewitness told local Palestinian media that Israeli forces "blew up a building without warning".
Speaking to The National, a local delivery driver said Israeli forces used a "shoulder-fired missile "to target a residential home – but the bakery was "in the way".
Palestinian state news agency Wafa said Israeli forces "blew up Al Kastoni's home and kidnapped two other Palestinians".
Jenin has been subject to several army raids in recent weeks, including one this month in which soldiers killed three Palestinians from the camp who were in their vehicles at the time, and another two-day raid in July when 12 people, including children, were killed and 140 others were injured.
The UN says at least 196 Palestinians have been killed by Israeli fire since January, including 40 children.