Kamel Ranaja, who died on Wednesday night, was reported to be a deputy to Mahmoud al-Mabhouh, who was killed in a Dubai hotel in 2010.
The Mossad was widely believed to be behind that assassination. It caused an international furore after Israeli agents were accused of using stolen passports cloned from British, Irish and other citizens to mount the operation.
A Hamas official told AFP that "a group of people entered the home of Kamel Ranaja, and killed him. According to information that we have gathered, the Mossad is behind the attack".
Ranaja's death was announced in a Hamas statement which said he died "in the service of his cause" and that his "blood would not be wasted".
Hamas's leader, Khaled Meshaal, is expected to attend Ranaja's funeral in Jordan on Thursday.
The Israeli defence minister, Ehud Barak, told Army Radio that Ranaja, also known as Nizar Abu Mujhad, "wasn't one of the righteous men of the generation", and there were probably many people interested in his death. The Mossad never comments on claims of its involvement in operations.
Since the Syrian uprising began 15 months ago, the exiled leadership of Hamas has largely abandoned its Damascus base. It is now scattered across Jordan, Egypt and the Gulf states.