"A home-made bomb damaged a car belonging to a military police officer which was parked in front of his house in Gaza City, without causing casualties," Gaza interior ministry spokesman Iyad al-Buzum said in a statement.
Witnesses said the car belonged to Helmi Khalaf, administrative and financial manager of the Hamas-run military police.
It was unclear who carried out the alleged attack.
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It came after Hamas police on Monday arrested several dozen hardline Islamist protesters who tried to storm the French cultural centre in Gaza City, threatening the lives of staff and chanting slogans against satirical magazine Charlie Hebdo.
A series of explosions in November targeted officials of Hamas's rivals Fatah, which is headed by Palestinian president Mahmud Abbas, but caused no injuries.
Observers have warned of the dangers of Hamas losing control inside Gaza to more radical Islamists including salafists with whom it has clashed in the past.
A 50-day war in Gaza between Hamas and Israel last year killed more than 2,200 people, destroyed tens of thousands of homes and left more than 100,000 people homeless.