The interior ministry in Gaza, run by Islamist movement Hamas, said it was shutting the Erez crossing for an indefinite period as it investigates Friday's murder.
It did not give details on the reason behind the closure, though there was speculation authorities may be seeking to prevent those responsible for the killing from leaving.
Hamas security forces were deployed along the Gazan borders and exits by sea were also banned, officials said.
He was killed by four bullets from a pistol equipped with a silencer.
Israel has not commented on the shooting.
According to Israeli media, Faqha was responsible for cells of Hamas's military wing, the Ezzedine al-Qassam Brigades, in the Israeli-occupied West Bank.
Today, Faqha's wife, Nahed Assida, called on "Palestinians in the West Bank and Gaza Strip to respond to this assassination."
"The price of my husband's blood is in your hands," she said during a women's conference in Gaza.
Ismail Haniya, until recently head of Hamas in Gaza, and Yahya Sinwar, who replaced him as leader, headed the procession.
According to Hamas, Faqha formed cells for the Islamist group's military wing in the West Bank cities of Tubas, also where he was born, and Jenin.
It said he played an important role in preparing two major attacks.
They included a suicide attack in the Israeli settlement neighbourhood of Gilo in east Jerusalem in 2002 that killed 19 people.
The second was a suicide bus attack later that year that killed nine people in the northern Israeli city of Safed.
Israel sentenced him to nine life sentences plus 50 years, but he was released in 2011 along with more than 1,000 other Palestinians in exchange for Gilad Shalit, an Israeli soldier Hamas had detained for five years, and transferred to Gaza.
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