An Israeli military spokesman confirmed that the raid had been called off because of the protest.
"The attack plan was cancelled because of the people there. We differentiate between innocent people and terrorists," he said.
Palestinian sources called the protest the first of its kind to have in effect prevented an air strike by the Israeli military.
Nour Odeh, Al Jazeera's correspondent in Gaza, reported that it was the first time such an act has been seen in the Gaza Strip by residents.
Baroud is accused of firing home-made rockets at Israel. Crowds of people stood on the rooftop and in the garden of the home.
The Israeli spokesman said that his country would continue its attacks against fighters, and accused them of using the civilians in the camp as human shields.
Nizar Rayan, a local Hamas leader who joined the protest, said: "We came here to protect this fighter, to protect his house and to prove that we are capable of defeating this Zionist policy."
The crowd chanted anti-Israel and anti-American slogans, and people said they were prepared to give their lives to protect the home.
"Yes to martyrdom. No to surrender," the crowd chanted.
Israel routinely orders residents out of their homes before air attacks on what it says are suspected weapons-storage facilities.
Odeh said: "This is a usual type of tactic from Israel in the Gaza Strip. They have been using it for months now. This is a type of psychological warfare.
"Weil Baroud is a member of a political faction that although not represented in parliament, does have a lot of support on the streets, especially in Gaza."