Mohammad Najar, 24, was riding a motorcycle east of Khan Younis in central Gaza when he was hit, Ma'an news agency reported.
The Islamic Jihad vowed to avenge his death in a statement it released saying "all options in response to the crime are available to us. Our martyr's blood will not be spilled in vain. We will respond at the right time and place," The Jerusalem Post said.
A statement released by the army said the operation was conducted together with Israel's security agency (Shin Bet) and said Najar was planning a large scale attack inside Israel.
Taher An-Nunu, a Gaza government spokesman, called on Palestinian factions in the Gaza Strip to comply with "what has been agreed upon," referring to calls by Hamas earlier this week to halt rocket attacks against Israel, Ma'an said.
On Tuesday morning a Qassam rocket fired from Gaza exploded in an open area south of Ashkelon, no injuries or damage was reported.