The shooting occurred within a few hours of a lorry-bomb attack near the Erez crossing, that left the assailant dead but caused no injuries, according to Israeli public radio.
At least three boys aged 12 to 15 were among the wounded, including one who was in a critical condition, said Muawiya Hassanein, the head of Gaza emergency services.
He said the man who died of bullet wounds was 22 years old.
Describing the Karni incident, Jacky Rowland, Al Jazeera's correspondent in Gaza, said: "Protesters had been called by Hamas to go to the crossing to protest against the siege.
"Karni is an important crossing into Gaza because commercial goods and aid enter the [Gaza] strip. And theoretically, it is also the place where Palestinian exporters should be able to send their goods to Israel.
"Because of the siege, there were no Palestinian exports. That is why people were protesting at Karni, very much drawing attention to the blockade of Gaza."
"Two incidents in one day aimed very much at the crossing points into Israel, have ... sought to highlight the issue of the blockade of the Gaza Strip."
Erez Bombing
The morning began with the lorry-bomb attack at the Erez crossing.
According to Israeli media reports, Israeli soldiers opened fire at the vehicle as it was approaching the terminal.
Abu Ahmed, a spokesman for the Islamic Jihad, said the group had carried out the attack in co-operation with the al-Aqsa Martyrs' Brigades, an offshoot of the Fatah faction.
Abu Ahmed said the lorry was carrying four tonnes of explosives. He identified the suicide bomber as 23-year-old Ibrahim Nasser from Jabalya in the northern Gaza Strip.
The driver of the lorry was killed in the blast.
An Israeli army spokeswoman said the lorry exploded on the Palestinian side of the frontier, blowing out windows in nearby buildings.
She said two other men involved in the attack were killed when two missiles launched from an Israeli helicopter destroyed their getaway vehicle.
New strategy
Al Jazeera's Rowland said the attack appeared to be a new, comparatively recent strategy by the armed groups in Gaza to carry out attacks targeting the border crossings with Israel.
"It wasn't very successful from the armed groups' point of view. The man tried to drive the truck laden with explosives detonated it well before reaching the Israel side of the crossing.
"Previous operations have had much more impact. An attack against the Nakhal Oz oil terminal earlier this month killed two people.
"On that occasion the groups really did expose a security flaw on the Israeli side."
Gaza incursion
Separately, but at the time of the Erez bombing, Israeli troops raided a village in the central Gaza Strip and shot dead a 63-year-old man, medical workers and Hamas said.
An Israeli military spokesman had no immediate information on the incident.
Israel frequently carries out raids and air strikes in the Gaza Strip as part of what it describes as efforts to curb cross-border rocket fire.
The incidents follow inconclusive ceasefire talks between Egyptian and Hamas officials in Cairo.
Hamas has demanded the crossings be reopened in return for a cessation of violence that has threatened to undermine peace talks between Mahmoud Abbas, the Palestinian president, and Ehud Olmert, the Israeli prime minister.
"Resistance is strong and we are not begging for calm," Abu Ahmed said after the attack.