The rocket fire came after Israeli jets carried out raids on tunnels under the Gaza-Egypt border earlier on Wednesday.
"Israeli Air Force aircraft hit a number of Hamas smuggling tunnels" in retaliation for the roadside bomb attack by Palestinians on the vehicle patrol the previous day, the Israeli army said in a statement on Wednesday.
An Israeli officer was killed and three other soldiers were wounded in the attack.
Three air raids took place before dawn, but no casualties were reported, local residents and Hamas security officials said.
Todd Baer, Al Jazeera's correspondent in Rafah, said: "People say this latest round of Israeli strikes started at around two o'clock this morning.
"They heard three strikes in a row. It hit this area hard. Fear is as high as it can be here."
Tunnels 'a lifeline'
The tunnels are used by Gazans to smuggle food, fuel and consumer goods from Egypt and are considered a lifeline for thousands of ordinary Gazans. Israel says Hamas uses them to re-arm.
Shortly after the bomb attack on Tuesday, Israel aircraft killed one Palestinian on a motorcycle in an air attack.
Hamas confirmed that one of its members was injured in the attack in the town of Khan Younis.
The exchanges were the first major military developments since Hamas and Israel declared separate ceasefires earlier this month after Israel's offensive against the Gaza Strip.
Ehud Olmert, the Israeli prime minister, later said the killing was only an initial reaction and that Israel's full response was still to come, Israeli media websites reported.
No Palestinian group has claimed responsibility for Tuesday's bomb attack.