The men, dressed in red prison jumpsuits, were shackled hand and foot and hooded as they were put to death at an exercise ground inside a police facility, an AFP correspondent reported.
Senior Hamas officials, representatives of other Gaza-based groups and a few journalists observed the hangings.
Hamas says that the Israeli intelligence agency Mossad and its Palestinian "collaborators" killed Mazen Faqha in the Palestinian territory on March 24, but has offered no evidence.
Israel has killed several Hamas leaders in the past and has accused Mazen Faqha of being behind several deadly bombing attacks against Israelis during the second Palestinian intifada, or uprising, of 2000-2005.
Hams says that Faqha formed units of the Islamist group's military wing in the West Bank cities of Tubas, where he was born, and Jenin.
The men who were hanged today were not implicated in his killing but were accused of past acts of "treason and collaborating", a Hamas interior ministry statement said.
They were aged 55, 42 and 31, the ministry said but did not name them.
The Islamist group has pledged "radical measures" against Palestinians who "collaborated" with Israel.
Hamas has offered "collaborators" a brief chance to turn themselves in and receive clemency.
"The doors of repentance will be open for one week, from Tuesday, April 4 to Tuesday, April 11," the interior ministry said on Tuesday.
Hamas also tightly restricted movement out of the enclave following the assassination.
The restrictions have stopped male patients aged between 15 and 45 from using the territory's sole crossing for people to enter Israel to receive medical treatment, Human Rights Watch said.
Security checks and searches have increased, including roadblocks.
The territory has been under an Israeli blockade for the past 10 years.
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