Foreign Minister Micheal Martin said an investigation had proved that eight Irish passports used in the operation were forgeries.
Hamas official Mahmoud al-Mabhouh was found dead in a Dubai hotel in January.
Dubai police have said they are 99% sure Israeli agents were involved, though Israel says there is no proof.
Mr Martin said in a statement that Israel had been “requested to withdraw a designated member of staff of its embassy” and that he expected the request would “be quickly acceded to”.
“The misuse of Irish passports by a state with which Ireland enjoys friendly, if sometimes frank, bilateral relations is clearly unacceptable and requires a firm response,” he said.
In Jerusalem, foreign ministry spokesman Yigal Palmor said the Israeli government regretted the Irish decision, which he said was “not in line with the importance of our relationship with the Irish government”.