A statement said al-Qassam Brigades executed Hassan Musallam who was convicted of providing information that helped Israel assassinate Hamas founder Sheik Ahmed Yassin earlier this year.
It said the group has a list of suspects and information about those involved in cooperation with Israel and "will punish them in proper time and place."
A Hamas spokesman said Musallam's execution "is meant to be a warning for other informers."
"Informers who come ahead, confess and ask for forgiveness during the current holy month of Ramadan would not be harmed physically," he added.
Israel assassinated several Hamas leaders, including Yassin's successor, Abdel Aziz Rantissi, who was killed in May a month after his predecessor's slaying.