But the Israeli army said only one soldier was moderately injured.
The explosion on Thursday threatened a fragile ceasefire between Israel and the Palestinians, and came just hours before the two sides were set to hold their first meeting on coordinating Israel's planned withdrawal from Gaza.
Thursday's bombing occurred on the Israeli side of the Karni crossing, the main transit point for cargo going in and out of Gaza, the army said.
It was not immediately clear how fighters planted the bomb. Gaza is enclosed by a fence that makes infiltrations extremely difficult.
Palestinian residents in the area said Israeli troops began firing machine guns after the explosion, and an army helicopter was seen landing in the area.
The ceasefire was declared by the Israeli and Palestinian leaders in February, and resistance groups agreed the following month to honour the truce.
There has been a sharp decline in fighting, but sporadic violence has persisted.
There was no immediate claim of responsibility for the bombing. But Palestinian fighters have threatened to avenge the deaths of three Palestinian youths killed by the army in southern Gaza earlier this month.
Shortly after the attack, the Palestinian Interior Ministry said it had opened an investigation. "Palestinian security is going to continue the investigation and work to fulfil all the obligations" made under the truce agreement, it said.