Baroud is charged with firing homemade rockets at Israel. Crowds of people stood on the rooftop and in the yard of the home.
Nour Odeh, Aljazeera's correspondent, reported that it was the first time such an act has been seen in the Gaza strip by residents, but could not say whether it would be enough to prevent an Israeli airstrike.
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.
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."
Israel routinely orders residents out of their homes ahead of airstrikes on suspected weapons-storage facilities, saying it wants to avoid casualties.
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 is not represented in parliament does have a lot of support on the streets, especially in Gaza."