The Palestinian was killed hours after rockets were fired from the launcher towards Israel on Wednesday, the army said.
Rescue services said two people, including a 15-year-old boy, were wounded in the rocket attack.
Earlier on Wednesday, Israel carried out an air strike on a house in Rafah in the southern Gaza Strip.
An Israeli military spokeswoman said: "There was an aerial attack on a house which was used as a facility to store weapons."
She added that residents had been told in advance to leave the building.
Witnesses said the house, which was destroyed in the early morning raid on Wednesday, belonged to a Palestinian activist and had been vacated before the attack.
"There was an aerial attack on a house which was used as a facility to store weapons"
An Israeli military spokeswoman
No casualties were reported in the air strike.
Hours later, an Israeli was moderately wounded by fragmentation from one of two rockets fired from the Gaza Strip by Palestinian fighters.
Israel has carried out frequent air strikes on the territory during an offensive carried out in late June, after gunmen from Gaza abducted a soldier in a cross-border raid.
More than 210 Palestinians, about half of them civilians, had been killed during the offensive, which Israel says was directed at stopping Palestinians from firing rockets into Israel.
Israeli troops raided a Jordanian-owned bank in the West Bank town of Nablus and several money-changing agencies in the occupied territory, local residents said on Wednesday.
An Israeli military source said soldiers raided "the financial infrastructure of terror organisations" during the night but declined to give further details.
The manager of al-Ahli Bank said troops blew open the front door and entered the premises. They were unable to open the safe and did not take anything of substance, although they caused damage to the bank's interior, he said.
"There is no justification for this action as we are operating as part of the accords between Israel, Jordan and the Palestinian Authority, and we are supervised by the Palestinian monetary authorities," Abd al-Latif Nasif said.
Local residents said troops confiscated large amounts of cash and computers belonging to money changers in Nablus, Tulkarm and Ramallah.